Supplementary Information

html version: Supplementary information

library(ggplot2)
library(ggforce)
library(ggpubr)
library(cowplot)
library(gridExtra)
library(colorspace)

library(gamlss)

library(kableExtra)

library(rsq)

library(sp)

library(dplyr)

fCO2.atm.2020 <- 411.51 * 1e-6 # oct 2020
fCO2.atm.2019 <- 408.75 * 1e-6 # oct 2019
fCO2.atm.2004 <- 374.63 * 1e-6 # oct 2004
fCO2.atm.1995 <- 360.17 * 1e-6

library(captioner)
fig_nums <- captioner() 
tab_nums <- captioner(prefix = "Table")

1 Import data

The data was prepared in Data preparation

norway <- readRDS("norway.rds")
nlss <- readRDS("nlss.rds")

norway$TOC_mg <- norway$TOC*12.011*1e3
norway$TOC_umol <- norway$TOC*1e6
norway$TA_ueq <- norway$TA * 1e6
norway$CA_ueq <- norway$CA * 1e6
norway$DIC_mg <- norway$DIC*12.011*1e3
norway$DIC_umol <- norway$DIC * 1e6
norway$CA_ueq <- norway$CA * 1e6
norway$Hplus_umol <- norway$Hplus *1e6
norway$invHplus_umol <- 1/norway$Hplus *1e6
norway$invHplus <- 1/norway$Hplus

ggplot()+
   geom_point(data = filter(norway, fCO2 > 2500*1e-6),aes(x=long, y = lat, col = survey), size = 6, shape = 1)+
  geom_point(data = filter(norway, fCO2 < 2500*1e-6),aes(x=long, y = lat, col = survey, size = fCO2*1e6))+
  borders(regions = c("Norway"))+ylim(57,63)+xlim(4,13)+
  scale_color_manual(values = c("firebrick","dodgerblue3"))+
 # scale_fill_continuous_divergingx(palette = "RdYlBu", aesthetics = c("fill","col"), mid = 30, rev = T)+ 
  labs(col="Survey", size = "pCO2, uatm")+
  theme_void()

Figure 1: Lakes sampled during the CBA survey (in red) and during the N112 survey (in red).

nlss <- readRDS("nlss.rds")
nlss$invHplus <- 1/nlss$Hplus
nlss$TOC_mg <- nlss$TOC*12.011*1e3

ggplot(nlss)+geom_point(aes(x=long, y = lat, col = TOC_mg))+
  borders(regions = c("Norway","Sweden","Finland"))+ylim(55,72)+xlim(4,32)+
  scale_fill_continuous_divergingx(palette = "RdYlBu", aesthetics = c("fill","col"), mid = 10, rev = T)+
  labs(x="TOC, mg/L")+
  theme_void()

Figure 2: Map of TOC in mg/L in the Northern Lake Survey

2 Estimation of organic and carbonate alkalinity

In this section, we investigate several ways of estimating the share of organic alkalinity in our samples.

2.1 Carbonate speciation N112 / CBA

The concentration of the carbonate species in the N112 and CBA survey is calculated directly from the measured partial pressure of \(CO_2\) (Appelo and Postma 2005):

\(pCO_2 = [H_2CO_3]/K_0\)

\([HCO3^-] = K_1 \times [H_2CO_3]/[H^+]\)

\([CO_3^{2-}] = K_2 \times [HCO_3 ^- ] / [H ^+]\)

\([TIC] = [H_2CO_3] + [HCO_3^-]+[CO_3 ^{2-}]\)

\(K_0\) is Henry’s constant from Weiss (1974). \(K_1\) and \(K_2\) are ionization constants of \(H_2CO_3\) and \(HCO_3^-\) , respectively obtained from Herbert S. Harned and Davis (1943) and Herbert S. Harned and Scholes (1941) and are adjusted for temperature.

In freshwater samples, the chemical activity of carbonate species is assumed to be equal to the molar concentration. Therefore, molar concentration is used in all equilibrium equations.

Liu, Butman, and Raymond (2020) reported that in water with low ionic strength, the pH is underestimated by 0.1 to 0.5 units.  We chose to not correct pH in this study because the ionic strength was not available for the N112 survey. Since only one lake in the Northern Lakes Survey had a pH inferior to 5, we assumed that the measurement errors would be minimal.

ggplot(norway, aes(x = pH))+
  geom_point(aes(y = H2CO3, col = "H2CO3"), alpha = 0.5)+
  geom_point(aes(y = HCO3, col = "HCO3"), alpha = 0.5)+
  geom_point(aes(y = CO3, col = "CO3"), alpha = 0.5)+
  labs(y = "Carbonate species (mol/L)", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3","orange"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

Figure 3: Concentration of carbonate species in mol/L in the CBA and N112 surveys

ggplot(norway,aes(x= pH))+geom_point(aes(y = ta_fCO2, col = "pCO2 from TA"), alpha = 0.5)+
  geom_point(aes(y = fCO2, col = "Measured pCO2"), alpha = 0.5)+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_bw(base_size = 15)+
  theme(legend.position = "bottom")

with(norway, cor(ta_fCO2, fCO2, use = "pairwise.complete.obs")^2)
with(subset(norway, pH > 5.4), cor(ta_fCO2, fCO2, use = "pairwise.complete.obs")^2)

Figure 4: Measured (red) and calculated (blue) pCO2 in atm for the CBA and N112 surveys

toc_boxplot <- ggplot(norway)+
  geom_boxplot(aes(x = "TOC", y = TOC, col = survey))+
  geom_boxplot(aes(x = "DIC", y = DIC, col = survey))+
  labs(x = "", y = "concentration, mol/L")+
  scale_color_manual(values = c("firebrick", "dodgerblue"))+
  theme_minimal()+
  theme(legend.position = "bottom")

toc_boxplot

Figure 5: Boxplot of DIC and TOC in mol/L for the CBA survey (red) and N112 survey (blue)

2.2 Organic alkalinity as OA = TA - CA

A simple method to estimate the organic alkalinity would be to substract the carbonate alkalinity, known thanks to the DIC measurement, to the total alkalinity. In a second step, one can investigate the link between the TOC concentration and this calculated organic alkalinity. This method is used in Couturier et al. (2022).

norway$OA <- with(norway, TA-CA)

ggarrange(
ggplot(norway)+geom_point(aes(x = pH, y = CA))+theme_bw(),
ggplot(norway)+geom_point(aes(x = pH, y = OA))+ylim(-1e-4, 1e-4)+theme_bw(),
ggplot(norway)+geom_point(aes(x = TOC, y = OA))+theme_bw(),
ggplot(norway)+geom_point(aes(x = TA, y = OA))+theme_bw(), nrow = 2, ncol = 2)

Figure 6: OA estimated as TA - CA, in eq/L

In our samples, there is no link between organic alkalinity calculated that way and the concentration of TOC. This might result from other sources of alkalinity in our samples.

2.3 Organic alkalinity according to Hruška et al. (2003)

Hruška et al. (2003) suggested that the organic alkalinity (OA) can be computed as a triprotic model. OA is the defined as the concentration of organic bases \([RCOO^-]\) in the solution, minus the concentration of organic bases at pH = 4.5, as for an end-point titration. \([RCOO^-]\) depends on three \(pK_a\) that were measured in Hruška et al. (2003):

\[[RCOO^-]=\alpha_1 \times \frac{m \times [TOC]}{3}+ \alpha_2 \times \frac{m \times [TOC]}{3} + \alpha_3 \times \frac{m \times [TOC]}{3}\]

Where α is the ionization fraction of each acid/base couple:

\[\alpha = \frac{[RCOO^-]}{[RCOOH]}=\frac{K_a}{[H^+} = \frac{10^{-pK_a}}{[H^+]}\]

And \(m\) is the site density of carboxylic group on the organic matter:

\[m = 10.2 \; \pm \; 0.6 \; \mu eq/mg \; DOC \Leftrightarrow 0.12 \; eq/mol \; DOC\]

\(m\) is supposed to be equally divided between the three acids with their respective \(pK_a\).

pKa1 <- 3.04
Ka1 <- 10^(-pKa1)

pKa2 <- 4.42
Ka2 <- 10^(-pKa2)

pKa3 <- 6.46
Ka3 <- 10^(-pKa3)

m <- 10.2*1e-6*12.011*1e3*1e-3# ueq/mg to eq/mol, site density BUT THERE IS A 1e3 PB: have to multiply by 1e-3 to stay in the range
norway$RCOO <- with(norway, (Ka1/Hplus + 2*Ka2/Hplus + 3*Ka3/Hplus)* m/3 * TOC) # estimated in eq/L

norway$RCOO_4.5 <- with(norway, (Ka1/10^(-4.5) + 2*Ka2/10^(-4.5) + 3*Ka3/10^(-4.5))* m/3 * TOC)

norway$OA_hruska <- with(norway, RCOO-RCOO_4.5)

ggplot(norway)+
  geom_point(aes(x = pH, y = RCOO, col = survey))+
  scale_color_manual(values = c("firebrick","dodgerblue3"))+
  labs(y="[RCOO-], mol/L")+
  theme_minimal()+
  theme(legend.position = "bottom")

norway$CA_hruska <- with(norway, TA - OA_hruska - OH + Hplus) 

norway$CO3_hruska <- with(norway,CA_hruska / (Hplus/K2 +2)) # in mol/L
norway$HCO3_hruska <- with(norway, CO3_hruska*Hplus/K2)
norway$H2CO3_hruska <- with(norway, HCO3_hruska*Hplus/K1)
norway$fCO2_hruska <- with(norway,H2CO3_hruska/K0)

with(norway, cor(fCO2_hruska, fCO2, use = "pairwise.complete.obs")^2)
with(subset(norway, pH > 5.4), cor(fCO2_hruska, fCO2, use = "pairwise.complete.obs")^2)

Figure 7: OA estimated with triprotic method of Hruska et al., in eq/L

ggplot(norway,aes(x= pH))+geom_point(aes(y = fCO2_hruska*1e6, col = "pCO2 from calculated from Hruska et al"), alpha = 0.5)+
  geom_point(aes(y = fCO2*1e6, col = "Measured pCO2"), alpha = 0.5)+
  labs(y = "pCO2, uatm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

Figure 8: pCO2 estimated with Hruska method, in atm

This method results in an overestimation of organic alkalinity in samples with high concentration of total organic carbon. The calculated carbonate alkalinity, and in turn the partial pressure of CO2, is then negative, which is impossible.

2.4 Organic alkalinity according to Liu, Butman, and Raymond (2020)

A simplifying approach was suggested by Liu, Butman, and Raymond (2020) , building on Cai, Wang, and Hodson (1998) and Lozovik (2005), where the organic alkalinity can be calculated directly from TOC as:

\(OA = 80 \% \times 10\% \times [TOC]\)

80% being the proportion of DOC that is an organic acid [@Cai1998], and 10% the maximum fraction of anions contributing to alkalinity (Lozovik 2005). This last value was calculated for DOC in humic lakes, but overall this equation is designed to be applicable to all kinds of lakes, tropical or temperate.

#norway$pH_Liu <- with(norway, pH - (0.03+0.05*log10(IS))) 
#norway$Hplus_Liu <- 10^(-norway$pH_Liu) 
#norway$OH_Liu <- with(norway,Kw*Hplus_Liu)

norway$OA_Liu <- 0.08 * norway$TOC
norway$CA_Liu <- with(norway, TA-OA_Liu - OH + Hplus)

norway$CO3_Liu <- with(norway,CA_Liu / (Hplus/K2 +2)) # in mol/L
norway$HCO3_Liu <- with(norway, CO3_Liu*Hplus/K2)
norway$H2CO3_Liu <- with(norway, HCO3_Liu*Hplus/K1)
norway$fCO2_Liu <- with(norway,H2CO3_Liu/K0)

norway$DIC_Liu <- with(norway, H2CO3_Liu + HCO3_Liu + CO3_Liu)

ggplot(norway,aes(x= pH))+geom_point(aes(y = fCO2_Liu, col = "pCO2 from calculated from Liu et al."), alpha = 0.5)+
  geom_point(aes(y = fCO2*1e6, col = "Measured pCO2"), alpha = 0.5)+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

Figure 9: pCO2 estimated with Liu method, in atm

Once again, the organic alkalinity is overestimated in samples with high concentration of TOC, resulting in negative pCO2.

3 Model DIC and pCO2

Since the different methods to adjust the total alkalinity by removing the share of organic alkalinity, we tried different models aiming at estimating either the concentration of dissolved inorganic carbon (DIC), in order to calculate pCO2 with the carbonate equilibrium, or directly the partial pressure of CO2.

For each set of predictors, we fitted a model for DIC, then calculated the resulting pCO2; and fitted a model for pCO2.

The models used here are generalized linear model, allowing the use of the Gamma distribution.

We added a fixed intercept in the pCO2 models corresponding to the atmospheric concentration of CO2.

3.1 TA

dic.ta <- glm(formula = DIC~TA, data = norway, family = Gamma(link = "identity"))

dic.ta.sum <- summary(dic.ta)$coefficients %>% as.data.frame() 
dic.ta.sp <- rownames(dic.ta.sum)[which(dic.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.ta.sum <- dic.ta.sum %>% format(scientific = T, digits = 2)

kable(dic.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	4.1e-05	3.3e-06	1.2e+01	6.9e-26
TA	1.3e+00	9.7e-02	1.3e+01	3.8e-27

norway$DIC_pred <- fitted(dic.ta)
norway$DIC_pred_res <- residuals(dic.ta)
dic.ta.r2 <- with(summary(dic.ta), 1 - deviance/null.deviance) %>% round(2)
dic.ta.aic <- AIC(dic.ta)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.ta.r2, ""))+
    theme_minimal(base_size = 15)

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
   coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
  theme_minimal(base_size = 15)

norway$pCO2_calc <- with(norway, DIC_pred/(K0*(1+K1*Hplus+K2*K1*Hplus^2)))

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 10: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA

nlss$dic_pred <- predict(dic.ta, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from modelled DIC"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 11: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.ta <- glm(formula = fCO2~TA+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.ta.sum <- summary(pco2.ta)$coefficients %>% as.data.frame() 
pco2.ta.sp <- rownames(pco2.ta.sum)[which(pco2.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.ta.sum <- pco2.ta.sum %>% format(scientific = T, digits = 2)

kable(pco2.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TA	6.3e+00	9.8e-01	6.5e+00	1e-09

norway$pCO2_pred <- fitted(pco2.ta)
norway$pCO2_pred_res <- residuals(pco2.ta)
pco2.ta.r2 <- with(summary(pco2.ta), 1 - deviance/null.deviance) %>% round(2)
pco2.ta.aic <- AIC(pco2.ta)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   
  labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 12: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) predicted (blue) pCO2 vs pH for pCO2~TA

nlss$pCO2_pred <- predict(pco2.ta, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "predicted pCO2 NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 13: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.2 1/TA

norway$invTA <- with(norway, ifelse(TA == 0, 0, 1/TA))

dic.invTA <- glm(formula = DIC~invTA, data = norway, family = Gamma(link = "identity"))

dic.invTA.sum <- summary(dic.invTA)$coefficients %>% as.data.frame() 
dic.invTA.sp <- rownames(dic.invTA.sum)[which(dic.invTA.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.invTA.sum <- dic.invTA.sum %>% format(scientific = T, digits = 2)

kable(dic.invTA.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	2.1e-04	2.8e-05	7.7e+00	1.2e-12
invTA	-3.5e-10	8.1e-11	-4.3e+00	2.9e-05

norway$DIC_pred <- fitted(dic.invTA)
norway$DIC_pred_res <- residuals(dic.invTA)
dic.invTA.r2 <- with(summary(dic.invTA), 1 - deviance/null.deviance) %>% round(2)
dic.invTA.aic <- AIC(dic.invTA)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.invTA.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
   coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
  theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0*(1+K1*Hplus+K2*K1*Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2, rel_heights = c(2,3))

Figure 14: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~1/TA

nlss$invTA <- with(nlss, ifelse(TA == 0, 0, 1/TA))

nlss$dic_pred <- predict(dic.invTA, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from modelled DIC"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 15: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.invTA <- glm(formula = fCO2~invTA+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.invTA.sum <- summary(pco2.invTA)$coefficients %>% as.data.frame() 
pco2.invTA.sp <- rownames(pco2.invTA.sum)[which(pco2.invTA.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.invTA.sum <- pco2.invTA.sum %>% format(scientific = T, digits = 2)

kable(pco2.invTA.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
invTA	2.3e-08	7.4e-09	3.1e+00	2.6e-03

norway$pCO2_pred <- fitted(pco2.invTA)
norway$pCO2_pred_res <- residuals(pco2.invTA)
pco2.invTA.r2 <- with(summary(pco2.invTA), 1 - deviance/null.deviance) %>% round(2)
pco2.invTA.aic <- AIC(pco2.invTA)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   
  labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.invTA.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 16: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) and predicted (blue) pCO2 vs pH for pCO2~1/TA

nlss$pCO2_pred <- predict(pco2.invTA, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "predicted pCO2 NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 17: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.4 TOC + temp

dic.toc.temp <- glm(formula = DIC~TOC+temp_k, data = norway, family = Gamma(link = "identity"))
dic.toc.temp.sum <- summary(dic.toc.temp)$coefficients %>% as.data.frame() 
dic.toc.temp.sp <- rownames(dic.toc.temp.sum)[which(dic.toc.temp.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.toc.temp.sum <- dic.toc.temp.sum %>% format(scientific = T, digits = 2)

kable(dic.toc.temp.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	1.4e-03	8.4e-04	1.6e+00	1.1e-01
TOC	3.0e-01	3.9e-02	7.6e+00	1.7e-12
temp_k	-4.8e-06	3.0e-06	-1.6e+00	1.1e-01

norway$DIC_pred <- fitted(dic.toc.temp)
norway$DIC_pred_res <- residuals(dic.toc.temp)
dic.toc.temp.r2 <- with(summary(dic.toc.temp), 1 - deviance/null.deviance) %>% round(2)
dic.toc.temp.aic <- AIC(dic.toc.temp)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.toc.temp.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 18: Predicted vs fitted values, Standardized residuals vs fitted values, and measured (red) calculated (blue) pCO2 vs pH for DIC~TOC

nlss$dic_pred <- predict(dic.toc.temp, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 19: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.toc.temp <- glm(formula = fCO2~TOC+temp_k+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.toc.temp.sum <- summary(pco2.toc.temp)$coefficients %>% as.data.frame() 
pco2.toc.temp.sp <- rownames(pco2.toc.temp.sum)[which(pco2.toc.temp.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.toc.temp.sum <- pco2.toc.temp.sum %>% format(scientific = T, digits = 2)

kable(pco2.toc.temp.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	9.4e-01	8.3e-02	1.1e+01	1.3e-22
temp_k	2.4e-07	1.3e-07	1.9e+00	6.4e-02

norway$pCO2_pred <- fitted(pco2.toc.temp)
norway$pCO2_pred_res <- residuals(pco2.toc.temp)
pco2.toc.temp.r2 <- with(summary(pco2.toc.temp), 1 - deviance/null.deviance) %>% round(2)
pco2.toc.temp.aic <- AIC(pco2.toc.temp)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.toc.temp.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 20: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) and predicted (blue), pCO2 vs pH for DIC~TOC

nlss$pCO2_pred <- predict(pco2.toc.temp, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 21: Predicted pCO2 in atm vs pH for the Northern Lake Survey

ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"), alpha = 0.5)+
  geom_point(aes(y = fCO2, col = "Measured pCO2"), alpha = 0.5)+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_bw(base_size = 15)+
  theme(legend.position = "bottom")

Figure 22: Model results for pCO2~TOC

3.5 TA + TOC

dic.toc.ta <- glm(formula = DIC~TOC+TA, data = norway, family = Gamma(link = "identity"))
dic.toc.ta.sum <- summary(dic.toc.ta)$coefficients %>% as.data.frame() 
dic.toc.ta.sp <- rownames(dic.toc.ta.sum)[which(dic.toc.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.toc.ta.sum <- dic.toc.ta.sum %>% format(scientific = T, digits = 2)

kable(dic.toc.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	3.0e-05	3.1e-06	9.6e+00	1.3e-17
TOC	3.2e-02	8.9e-03	3.6e+00	3.9e-04
TA	1.2e+00	9.6e-02	1.2e+01	5.9e-25

norway$DIC_pred <- fitted(dic.toc.ta)
norway$DIC_pred_res <- residuals(dic.toc.ta)
dic.toc.ta.r2 <- with(summary(dic.toc.ta), 1 - deviance/null.deviance) %>% round(2)
dic.toc.ta.aic <- AIC(dic.toc.ta)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.toc.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 23: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA+TOC

nlss$dic_pred <- predict(dic.toc.ta, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 24: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.toc.ta <- glm(formula = fCO2~TOC+TA+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.toc.ta.sum <- summary(pco2.toc.ta)$coefficients %>% as.data.frame() 
pco2.toc.ta.sp <- rownames(pco2.toc.ta.sum)[which(pco2.toc.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.toc.ta.sum <- pco2.toc.ta.sum %>% format(scientific = T, digits = 2)

kable(pco2.toc.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	9.0e-01	7.9e-02	1.1e+01	9.3e-23
TA	8.3e-01	3.7e-01	2.3e+00	2.4e-02

norway$pCO2_pred <- fitted(pco2.toc.ta)
norway$pCO2_pred_res <- residuals(pco2.toc.ta)
pco2.toc.ta.r2 <- with(summary(pco2.toc.ta), 1 - deviance/null.deviance) %>% round(2)
pco2.toc.ta.aic <- AIC(pco2.toc.ta)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.toc.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 25: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for pCO2~TOC+TA `

nlss$pCO2_pred <- predict(pco2.toc.ta, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 26: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.6 TA*TOC + Hplus

dic.tocta.Hplus <- glm(formula = DIC~TOC+TA+Hplus, data = norway, family = Gamma(link = "identity"))
  dic.tocta.Hplus.sum <- summary(dic.tocta.Hplus)$coefficients %>% as.data.frame() 
  dic.tocta.Hplus.sp <- rownames(dic.tocta.Hplus.sum)[which(dic.tocta.Hplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
  dic.tocta.Hplus.sum <- dic.tocta.Hplus.sum %>% format(scientific = T, digits = 2)

kable(dic.tocta.Hplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	1.9e-05	3.8e-06	5.1e+00	8.0e-07
TOC	5.2e-03	7.5e-03	6.9e-01	4.9e-01
TA	1.4e+00	1.1e-01	1.3e+01	9.2e-28
Hplus	3.7e+00	8.4e-01	4.3e+00	2.4e-05

norway$DIC_pred <- fitted(dic.tocta.Hplus)
norway$DIC_pred_res <- residuals(dic.tocta.Hplus)
dic.tocta.Hplus.r2 <- with(summary(dic.tocta.Hplus), 1 - deviance/null.deviance) %>% round(2)
dic.tocta.Hplus.aic <- AIC(dic.tocta.Hplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.tocta.Hplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 27: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA x TOC + Hplus

nlss$dic_pred <- predict(dic.tocta.Hplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 28: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.tocta.Hplus <- glm(formula = fCO2~TOC+TA+Hplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.tocta.Hplus.sum <- summary(pco2.tocta.Hplus)$coefficients %>% as.data.frame() 
pco2.tocta.Hplus.sp <- rownames(pco2.tocta.Hplus.sum)[which(pco2.tocta.Hplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.tocta.Hplus.sum <- pco2.tocta.Hplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.tocta.Hplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	6.7e-01	8.7e-02	7.7e+00	8.8e-13
TA	1.5e+00	4.2e-01	3.6e+00	4.0e-04
Hplus	2.9e+01	8.5e+00	3.4e+00	7.6e-04

norway$pCO2_pred <- fitted(pco2.tocta.Hplus)
norway$pCO2_pred_res <- residuals(pco2.tocta.Hplus)
pco2.tocta.Hplus.r2 <- with(summary(pco2.tocta.Hplus), 1 - deviance/null.deviance) %>% round(2)
pco2.tocta.Hplus.aic <- AIC(pco2.tocta.Hplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.tocta.Hplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 29: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for pCO2~TA x TOC + Hplus

nlss$pCO2_pred <- predict(pco2.tocta.Hplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 30: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.7 TOC + pH

dic.toc.Hplus <- glm(formula = DIC~TOC+Hplus, data = norway, family = Gamma(link = "identity"))
dic.toc.Hplus.sum <- summary(dic.toc.Hplus)$coefficients %>% as.data.frame() 
dic.toc.Hplus.sp <- rownames(dic.toc.Hplus.sum)[which(dic.toc.Hplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.toc.Hplus.sum <- dic.toc.Hplus.sum %>% format(scientific = T, digits = 2)

kable(dic.toc.Hplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	3.5e-05	1.0e-05	3.4e+00	7.9e-04
TOC	2.6e-01	3.6e-02	7.5e+00	4.3e-12
Hplus	-4.4e+00	1.6e+00	-2.7e+00	7.8e-03

norway$DIC_pred <- fitted(dic.toc.Hplus)
norway$DIC_pred_res <- residuals(dic.toc.Hplus)
dic.toc.Hplus.r2 <- with(summary(dic.toc.Hplus), 1 - deviance/null.deviance) %>% round(2)
dic.toc.Hplus.aic <- AIC(dic.toc.Hplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.toc.Hplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "Hplus", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 31: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TOC+Hplus

nlss$dic_pred <- predict(dic.toc.Hplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 32: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.toc.Hplus <- glm(formula = fCO2~TOC+Hplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.toc.Hplus.sum <- summary(pco2.toc.Hplus)$coefficients %>% as.data.frame() 
pco2.toc.Hplus.sp <- rownames(pco2.toc.Hplus.sum)[which(pco2.toc.Hplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.toc.Hplus.sum <- pco2.toc.Hplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.toc.Hplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	9.9e-01	6.8e-02	1.5e+01	1.2e-31
Hplus	1.5e+01	8.0e+00	1.9e+00	5.4e-02

norway$pCO2_pred <- fitted(pco2.toc.Hplus)
norway$pCO2_pred_res <- residuals(pco2.toc.Hplus)
pco2.toc.Hplus.r2 <- with(summary(pco2.toc.Hplus), 1 - deviance/null.deviance) %>% round(2)
pCO2.toc.Hplus.aic <- AIC(pco2.toc.Hplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.toc.Hplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 31: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TOC+Hplus

nlss$pCO2_pred <- predict(pco2.toc.Hplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 33: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.8 TA * TOC

dic.tocta <- glm(formula = DIC~TOC*TA, data = norway, family = Gamma(link = "identity"))
dic.tocta.sum <- summary(dic.tocta)$coefficients %>% as.data.frame() 
dic.tocta.sp <- rownames(dic.tocta.sum)[which(dic.toc.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.tocta.sum <- dic.tocta.sum %>% format(scientific = T, digits = 2)

kable(dic.tocta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	3.0e-05	3.5e-06	8.6e+00	6.5e-15
TOC	3.2e-02	1.0e-02	3.1e+00	2.1e-03
TA	1.2e+00	1.4e-01	8.1e+00	1.2e-13
TOC:TA	4.0e+00	1.4e+02	2.9e-02	9.8e-01

norway$DIC_pred <- fitted(dic.tocta)
norway$DIC_pred_res <- residuals(dic.tocta)
dic.tocta.r2 <- with(summary(dic.tocta), 1 - deviance/null.deviance) %>% round(2)
dic.tocta.aic <- AIC(dic.tocta)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.tocta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 34: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA x TOC

nlss$dic_pred <- predict(dic.tocta, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 35: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.tocta <- glm(formula = fCO2~TOC+TA+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.tocta.sum <- summary(pco2.tocta)$coefficients %>% as.data.frame() 
pco2.tocta.sp <- rownames(pco2.tocta.sum)[which(pco2.tocta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.tocta.sum <- pco2.tocta.sum %>% format(scientific = T, digits = 2)

kable(pco2.tocta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	9.0e-01	7.9e-02	1.1e+01	9.3e-23
TA	8.3e-01	3.7e-01	2.3e+00	2.4e-02

norway$pCO2_pred <- fitted(pco2.tocta)
norway$pCO2_pred_res <- residuals(pco2.tocta)
pco2.tocta.r2 <- with(summary(pco2.tocta), 1 - deviance/null.deviance) %>% round(2)
pco2.tocta.aic <- AIC(pco2.tocta)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.tocta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 36: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for pCO2~TA x TOC

nlss$pCO2_pred <- predict(pco2.tocta, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 37: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.9 TA*Hplus

dic.taHplus <- glm(formula = DIC~TA*Hplus, data = norway, family = Gamma(link = "identity"))

dic.taHplus.sum <- summary(dic.taHplus)$coefficients %>% as.data.frame() 
dic.taHplus.sp <- rownames(dic.taHplus.sum)[which(dic.taHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.taHplus.sum <- dic.taHplus.sum %>% format(scientific = T, digits = 2)

kable(dic.taHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	1.8e-05	3.9e-06	4.7e+00	4.8e-06
TA	1.4e+00	9.3e-02	1.5e+01	6.3e-33
Hplus	4.0e+00	7.8e-01	5.1e+00	8.7e-07
TA:Hplus	1.1e+05	1.1e+05	1.0e+00	3.0e-01

norway$DIC_pred <- fitted(dic.taHplus)
norway$DIC_pred_res <- residuals(dic.taHplus)
dic.taHplus.r2 <- with(summary(dic.taHplus), 1 - deviance/null.deviance) %>% round(2)
dic.taHplus.aic <- AIC(dic.taHplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.taHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 38: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA x Hplus

nlss$dic_pred <- predict(dic.taHplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 39: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.taHplus <- glm(formula = fCO2~TA*Hplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.taHplus.sum <- summary(pco2.taHplus)$coefficients %>% as.data.frame() 
pco2.taHplus.sp <- rownames(pco2.taHplus.sum)[which(pco2.taHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.taHplus.sum <- pco2.taHplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.taHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TA	2.7e+00	3.3e-01	8.0e+00	1.7e-13
Hplus	5.2e+01	7.1e+00	7.3e+00	8.2e-12
TA:Hplus	9.7e+06	1.3e+06	7.4e+00	7.2e-12

norway$pCO2_pred <- fitted(pco2.taHplus)
norway$pCO2_pred_res <- residuals(pco2.taHplus)
pco2.taHplus.r2 <- with(summary(pco2.taHplus), 1 - deviance/null.deviance) %>% round(2)
pco2.taHplus.aic <- AIC(pco2.taHplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.taHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 40: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA

nlss$pCO2_pred <- predict(pco2.taHplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 41: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.10 TOC*Hplus

dic.TOCHplus <- glm(formula = DIC~TOC*Hplus, data = norway, family = Gamma(link = "identity"))

dic.TOCHplus.sum <- summary(dic.TOCHplus)$coefficients %>% as.data.frame() 
dic.TOCHplus.sp <- rownames(dic.TOCHplus.sum)[which(dic.TOCHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.TOCHplus.sum <- dic.TOCHplus.sum %>% format(scientific = T, digits = 2)

kable(dic.TOCHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	2.5e-05	1.0e-05	2.4e+00	1.6e-02
TOC	2.9e-01	3.8e-02	7.4e+00	4.6e-12
Hplus	-1.6e+00	2.4e+00	-6.4e-01	5.3e-01
TOC:Hplus	-7.2e+03	4.0e+03	-1.8e+00	7.2e-02

norway$DIC_pred <- fitted(dic.TOCHplus)
norway$DIC_pred_res <- residuals(dic.TOCHplus)
dic.TOCHplus.r2 <- with(summary(dic.TOCHplus), 1 - deviance/null.deviance) %>% round(2)
dic.TOCHplus.aic <- AIC(dic.TOCHplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.TOCHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 42: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TOC x Hplus

nlss$dic_pred <- predict(dic.TOCHplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 43: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.TOCHplus <- glm(formula = fCO2~TOC*Hplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.TOCHplus.sum <- summary(pco2.TOCHplus)$coefficients %>% as.data.frame() 
pco2.TOCHplus.sp <- rownames(pco2.TOCHplus.sum)[which(pco2.TOCHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.TOCHplus.sum <- pco2.TOCHplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.TOCHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	9.9e-01	7.1e-02	1.4e+01	3.5e-30
Hplus	1.6e+01	1.2e+01	1.4e+00	1.6e-01
TOC:Hplus	-2.9e+03	2.5e+04	-1.1e-01	9.1e-01

norway$pCO2_pred <- fitted(pco2.TOCHplus)
norway$pCO2_pred_res <- residuals(pco2.TOCHplus)
pco2.TOCHplus.r2 <- with(summary(pco2.TOCHplus), 1 - deviance/null.deviance) %>% round(2)
pco2.TOCHplus.aic <- AIC(pco2.TOCHplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.TOCHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 42: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TOC x Hplus

nlss$pCO2_pred <- predict(pco2.TOCHplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 43: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.11 TA + TOC*Hplus

dic.tocHplus.ta <- glm(formula = DIC~TOC*Hplus+TA, data = norway, family = Gamma(link = "identity"))
dic.tocHplus.ta.sum <- summary(dic.tocHplus.ta)$coefficients %>% as.data.frame() 
dic.tocHplus.ta.sp <- rownames(dic.tocHplus.ta.sum)[which(dic.tocHplus.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.tocHplus.ta.sum <- dic.tocHplus.ta.sum %>% format(scientific = T, digits = 2)

kable(dic.tocHplus.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	2.5e-05	4.3e-06	5.8e+00	2.8e-08
TOC	-6.0e-03	5.9e-03	-1.0e+00	3.1e-01
Hplus	1.4e+00	1.2e+00	1.2e+00	2.4e-01
TA	1.4e+00	1.0e-01	1.4e+01	4.1e-30
TOC:Hplus	4.5e+03	2.0e+03	2.3e+00	2.4e-02

norway$DIC_pred <- fitted(dic.tocHplus.ta)
norway$DIC_pred_res <- residuals(dic.tocHplus.ta)
dic.tocHplus.ta.r2 <- with(summary(dic.tocHplus.ta), 1 - deviance/null.deviance) %>% round(2)
dic.tocHplus.ta.aic <- AIC(dic.tocHplus.ta)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.tocHplus.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 44: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC ~ TA + TOC x Hplus

nlss$dic_pred <- predict(dic.tocHplus.ta, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 45: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.tocHplus.ta <- glm(formula = fCO2~TOC*Hplus+TA+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.tocHplus.ta.sum <- summary(pco2.tocHplus.ta)$coefficients %>% as.data.frame() 
pco2.tocHplus.ta.sp <- rownames(pco2.tocHplus.ta.sum)[which(pco2.tocHplus.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.tocHplus.ta.sum <- pco2.tocHplus.ta.sum %>% format(scientific = T, digits = 2)

kable(pco2.tocHplus.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	5.6e-01	9.1e-02	6.2e+00	5.3e-09
Hplus	1.7e+01	1.2e+01	1.5e+00	1.3e-01
TA	1.9e+00	4.5e-01	4.2e+00	3.6e-05
TOC:Hplus	5.0e+04	2.9e+04	1.8e+00	7.9e-02

norway$pCO2_pred <- fitted(pco2.tocHplus.ta)
norway$pCO2_pred_res <- residuals(pco2.tocHplus.ta)
pco2.tocHplus.ta.r2 <- with(summary(pco2.tocHplus.ta), 1- deviance/null.deviance) %>% round(2)
pco2.tocHplus.ta.aic <- AIC(pco2.tocHplus.ta)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.tocHplus.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 44: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC ~ TA + TOC x Hplus

nlss$pCO2_pred <- predict(pco2.tocHplus.ta, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 45: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.12 TOC + TA*Hplus

dic.toc.taHplus <- glm(formula = DIC~TOC+TA*Hplus, data = norway, family = Gamma(link = "identity"))

dic.toc.taHplus.sum <- summary(dic.toc.taHplus)$coefficients %>% as.data.frame() 
dic.toc.taHplus.sp <- rownames(dic.toc.taHplus.sum)[which(dic.toc.taHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.toc.taHplus.sum <- dic.toc.taHplus.sum %>% format(scientific = T, digits = 2)
kable(dic.toc.taHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	1.8e-05	3.9e-06	4.7e+00	5.7e-06
TOC	-4.0e-04	6.9e-03	-5.8e-02	9.5e-01
TA	1.4e+00	1.0e-01	1.3e+01	1.8e-28
Hplus	4.0e+00	8.4e-01	4.8e+00	3.9e-06
TA:Hplus	1.1e+05	1.1e+05	1.0e+00	3.2e-01

norway$DIC_pred <- fitted(dic.toc.taHplus)
norway$DIC_pred_res <- residuals(dic.toc.taHplus)
dic.toc.taHplus.r2 <- with(summary(dic.toc.taHplus), 1 - deviance/null.deviance) %>% round(2)
dic.toc.taHplus.aic <- AIC(dic.toc.taHplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.toc.taHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 46: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC ~ TOC + TA x Hplus

nlss$dic_pred <- predict(dic.toc.taHplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 47: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.toc.taHplus <- glm(formula = fCO2~TOC+TA*Hplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.toc.taHplus.sum <- summary(pco2.toc.taHplus)$coefficients %>% as.data.frame()
pco2.toc.taHplus.sp <- rownames(pco2.toc.taHplus.sum)[which(pco2.toc.taHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.toc.taHplus.sum <- pco2.toc.taHplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.toc.taHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	-1.4e-02	2.7e-02	-5.3e-01	6.0e-01
TA	2.7e+00	3.5e-01	7.7e+00	1.1e-12
Hplus	5.3e+01	7.2e+00	7.4e+00	8.1e-12
TA:Hplus	9.9e+06	1.4e+06	7.3e+00	1.1e-11

norway$pCO2_pred <- fitted(pco2.toc.taHplus)
norway$pCO2_pred_res <- residuals(pco2.toc.taHplus)
pco2.toc.taHplus.r2 <- with(summary(pco2.toc.taHplus), 1 - deviance/null.deviance) %>% round(2)
pco2.toc.taHplus.aic <- AIC(pco2.toc.taHplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.toc.taHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 48: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for pCO2~TOC + TA x Hplus

nlss$pCO2_pred <- predict(pco2.toc.taHplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 49: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.13 TOC + TA*invHplus

norway$invHplus <- with(norway, 1/Hplus)

dic.toc.tainvHplus <- glm(formula = DIC~TOC+TA*invHplus, data = norway, family = Gamma(link = "identity"))

dic.toc.tainvHplus.sum <- summary(dic.toc.tainvHplus)$coefficients %>% as.data.frame()
dic.toc.tainvHplus.sp <- rownames(dic.toc.tainvHplus.sum)[which(dic.toc.tainvHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.toc.tainvHplus.sum <- dic.toc.tainvHplus.sum %>% format(scientific = T, digits = 2)

kable(dic.toc.tainvHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	3.4e-05	2.6e-06	1.3e+01	7.4e-27
TOC	4.1e-02	7.2e-03	5.7e+00	6.1e-08
TA	5.0e-01	1.2e-01	4.2e+00	3.7e-05
invHplus	-4.2e-12	1.9e-12	-2.2e+00	2.9e-02
TA:invHplus	8.2e-08	1.2e-08	6.9e+00	1.0e-10

norway$DIC_pred <- fitted(dic.toc.tainvHplus)
norway$DIC_pred_res <- residuals(dic.toc.tainvHplus)
dic.toc.tainvHplus.r2 <- with(summary(dic.toc.tainvHplus), 1 - deviance/null.deviance) %>% round(2)
dic.toc.tainvHplus.aic <- AIC(dic.toc.tainvHplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.toc.tainvHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 50: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TOC + TA/hplus

nlss$dic_pred <- predict(dic.toc.tainvHplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 51: Predicted pCO2 in atm vs pH for the Northern Lake Survey

norway$invHplus <- with(norway, 1/Hplus)

pco2.toc.tainvHplus <- glm(formula = fCO2~TOC+TA*invHplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.toc.tainvHplus.sum <- summary(pco2.toc.tainvHplus)$coefficients %>% as.data.frame() 
pco2.toc.tainvHplus.sp <- rownames(pco2.toc.tainvHplus.sum)[which(pco2.toc.tainvHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.toc.tainvHplus.sum <- pco2.toc.tainvHplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.toc.tainvHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	8.7e-01	9.0e-02	9.7e+00	6.5e-18
TA	1.9e+00	8.1e-01	2.4e+00	1.8e-02
invHplus	-1.4e-11	6.9e-12	-2.1e+00	3.8e-02
TA:invHplus	-1.2e-08	1.9e-08	-6.1e-01	5.4e-01

norway$pCO2_pred <- fitted(pco2.toc.tainvHplus)
norway$pCO2_pred_res <- residuals(pco2.toc.tainvHplus)
pco2.toc.tainvHplus.r2 <- with(summary(pco2.toc.tainvHplus), 1 - deviance / null.deviance) %>% round(2)
pco2.toc.tainvHplus.aic <- AIC(pco2.toc.tainvHplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.toc.tainvHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
   coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

*Figure 52: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA

nlss$pCO2_pred <- predict(pco2.toc.tainvHplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 53: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.14 TA + TOC*invHplus

norway$invHplus <- with(norway, 1/Hplus)

dic.tocinvHplus.ta <- glm(formula = DIC~TOC*invHplus+TA, data = norway, family = Gamma(link = "identity"))

dic.tocinvHplus.ta.sum <- summary(dic.tocinvHplus.ta)$coefficients %>% as.data.frame() 
dic.tocinvHplus.ta.sp <- rownames(dic.tocinvHplus.ta.sum)[which(dic.tocinvHplus.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.tocinvHplus.ta.sum <- dic.tocinvHplus.ta.sum %>% format(scientific = T, digits = 2)

kable(dic.tocinvHplus.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	2.9e-05	3.2e-06	9.0e+00	5.9e-16
TOC	4.0e-02	9.4e-03	4.3e+00	3.3e-05
invHplus	2.9e-12	2.6e-12	1.1e+00	2.6e-01
TA	5.9e-01	1.5e-01	4.0e+00	9.9e-05
TOC:invHplus	1.1e-08	3.5e-09	3.1e+00	2.6e-03

norway$DIC_pred <- fitted(dic.tocinvHplus.ta)
norway$DIC_pred_res <- residuals(dic.tocinvHplus.ta)
dic.tocinvHplus.ta.r2 <- with(summary(dic.tocinvHplus.ta), 1 - deviance/null.deviance) %>% round(2)
dic.tocinvHplus.ta.aic <- AIC(dic.tocinvHplus.ta)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.tocinvHplus.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+   
    coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3+labs(caption = ),nrow = 2,rel_heights = c(2,3))

Figure 54: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC ~ TOC / Hplus + TA

nlss$dic_pred <- predict(dic.tocinvHplus.ta, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 55: Predicted pCO2 in atm vs pH for the Northern Lake Survey

norway$invHplus <- with(norway, 1/Hplus)

pco2.tocinvHplus.ta <- glm(formula = fCO2~TOC*invHplus+TA+0+offset(fCO2.atm), data = norway, start = c(0,0,0,0), family = Gamma(link = "identity"))

pco2.tocinvHplus.ta.sum <- summary(pco2.tocinvHplus.ta)$coefficients %>% as.data.frame() 
pco2.tocinvHplus.ta.sp <- rownames(pco2.tocinvHplus.ta.sum)[which(pco2.tocinvHplus.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.tocinvHplus.ta.sum <- pco2.tocinvHplus.ta.sum %>% format(scientific = T, digits = 2)
  

kable(pco2.tocinvHplus.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	8.8e-01	8.0e-02	1.1e+01	1.3e-21
invHplus	-8.8e-12	8.0e-12	-1.1e+00	2.8e-01
TA	1.9e+00	6.1e-01	3.2e+00	1.5e-03
TOC:invHplus	-1.5e-08	1.1e-08	-1.3e+00	1.9e-01

norway$pCO2_pred <- fitted(pco2.tocinvHplus.ta)
norway$pCO2_pred_res <- residuals(pco2.tocinvHplus.ta)
pco2.tocinvHplus.ta.r2 <- with(summary(pco2.tocinvHplus.ta), 1 - deviance/null.deviance) %>% round(2)
pco2.tocinvHplus.ta.aic <- AIC(pco2.tocinvHplus.ta)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.tocinvHplus.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 56: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for pCO2 ~ TOC / Hplus + TA

nlss$pCO2_pred <- predict(pco2.tocinvHplus.ta, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 37: Predicted pCO2 in atm vs pH for the Northern Lake Survey

3.15 Summary of all models

Table 1: Summary of DIC and pCO2 models

kable(cbind(data.frame(Predictors = c("TA",
                                      "1/TA",
                                "TOC",
                                "TA + TOC",
                                "TA*TOC",
                                "TA*Hplus",
                                "TOC*Hplus",
                                "TA*Hplus + TOC", 
                                "TA + TOC*Hplus",
                                "TA/Hplus + TOC",
                                "TA + TOC/Hplus"),
                        R2 = c(pco2.ta.r2,
                              pco2.invTA.r2,
                              pco2.toc.r2,
                              pco2.toc.ta.r2,
                              pco2.tocta.r2,
                              pco2.taHplus.r2,
                              pco2.TOCHplus.r2,
                              pco2.toc.taHplus.r2,
                              pco2.tocHplus.ta.r2,
                              pco2.toc.tainvHplus.r2,
                              pco2.tocinvHplus.ta.r2),
                       AIC = c(pco2.ta.aic,
                              pco2.invTA.aic,
                              pco2.toc.aic,
                              pco2.toc.ta.aic,
                              pco2.tocta.aic,
                              pco2.taHplus.aic,
                              pco2.TOCHplus.aic,
                              pco2.toc.taHplus.aic,
                              pco2.tocHplus.ta.aic,
                              pco2.toc.tainvHplus.aic,
                              pco2.tocinvHplus.ta.aic),
                        significant  = c(pco2.ta.sp,
                                 pco2.invTA.sp,
                                 pco2.toc.sp,
                                 pco2.toc.ta.sp,
                                 pco2.tocta.sp,
                                 pco2.taHplus.sp,
                                 pco2.TOCHplus.sp,
                                 pco2.toc.taHplus.sp,
                                 pco2.tocHplus.ta.sp,
                                 pco2.toc.tainvHplus.sp,
                                 pco2.tocinvHplus.ta.sp)),
                data.frame(R2 = c(dic.ta.r2,
                                dic.invTA.r2,
                                dic.toc.r2,
                                dic.toc.ta.r2,
                                dic.tocta.r2,
                                dic.taHplus.r2,
                                dic.TOCHplus.r2,
                                dic.toc.taHplus.r2,
                                dic.tocHplus.ta.r2,
                                dic.toc.tainvHplus.r2,
                                dic.tocinvHplus.ta.r2),
                           AIC = c(dic.ta.aic,
                                dic.invTA.aic,
                                dic.toc.aic,
                                dic.toc.ta.aic,
                                dic.tocta.aic,
                                dic.taHplus.aic,
                                dic.TOCHplus.aic,
                                dic.toc.taHplus.aic,
                                dic.tocHplus.ta.aic,
                                dic.toc.tainvHplus.aic,
                                dic.tocinvHplus.ta.aic),
                      significant  = c(dic.ta.sp,
                                dic.invTA.sp,
                                dic.toc.sp,
                                dic.toc.ta.sp,
                                dic.tocta.sp,
                                dic.taHplus.sp,
                                dic.TOCHplus.sp,
                                dic.toc.taHplus.sp,
                                dic.tocHplus.ta.sp,
                                dic.toc.tainvHplus.sp,
                                dic.tocinvHplus.ta.sp))),
             digits = 2) %>% 
  add_header_above(c(" "= 1, "pCO2" = 3, "DIC" = 3),italic = T) %>%
  column_spec(column = c(2,4), bold = T) %>% 
  kable_styling(bootstrap_options = "bordered")

	pCO2			DIC
Predictors	R2	AIC	significant	R2	AIC	significant
TA	0.71	-2039.91	TA	0.82	-2915.00	(Intercept), TA
1/TA	0.17	-1829.24	invTA	0.05	-2600.20	(Intercept), invTA
TOC	0.88	-2192.88	TOC	0.45	-2709.82	(Intercept), TOC
TA + TOC	0.88	-2197.09	TOC, TA	0.84	-2933.13	(Intercept), TOC, TA
TA*TOC	0.88	-2197.09	TOC, TA	0.84	-2931.13
TA*Hplus	0.90	-2236.16	TA, Hplus, TA:Hplus	0.86	-2952.38	(Intercept), TA, Hplus
TOC*Hplus	0.88	-2193.20	TOC	0.50	-2724.46	(Intercept), TOC
TA*Hplus + TOC	0.90	-2234.25	TA, Hplus, TA:Hplus	0.86	-2950.38	(Intercept), TA, Hplus
TA + TOC*Hplus	0.89	-2208.10	TOC, TA	0.86	-2955.67	(Intercept), TA, TOC:Hplus
TA/Hplus + TOC	0.88	-2195.90	TOC, TA, invHplus	0.89	-2992.33	(Intercept), TOC, TA, invHplus, TA:invHplus
TA + TOC/Hplus	0.88	-2197.22	TOC, TA	0.85	-2947.14	(Intercept), TOC, TA, TOC:invHplus

4 Northern European Lakes Survey

4.1 Predict pCO2

nlss$ta_CO3 <- with(nlss,(TA - OH + Hplus) / (Hplus/K2 +2)) # in mol/L
nlss$ta_HCO3 <- with(nlss, ta_CO3*Hplus/K2)
nlss$ta_H2CO3 <- with(nlss, ta_HCO3*Hplus/K1)
nlss$pCO2_ta <- with(nlss,ta_H2CO3/K0)

g1 <- ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_ta), alpha = 0.5, col = "firebrick")+
  labs(x = "pH", y = "pCO2 from TA, atm")+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  facet_zoom(y = pCO2_ta > 0, zoom.size = 1)+
  theme_bw(base_size = 15)

print(g1)

Figure 57: pCO2 calculated from TA in the NLS surveys

nlss$pCO2_toc <- predict(pco2.toc, newdata = nlss, type = "response")
nlss$pCO2_toc.se <- predict(pco2.toc, newdata = nlss, type = "response", se.fit = T)$se.fit


g1 <- ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_ta*1e6, col = "pCO2 from carbonate equilibrium"), alpha = 0.5)+
  geom_point(aes(y = pCO2_toc*1e6, col = "pCO2 modelled with TOC"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, uatm")+
  scale_color_manual(values = c("firebrick","dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")+
  facet_zoom(y = pCO2_ta > 0, zoom.size = 2)


g2 <- ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_ta*1e6, col = "pCO2 from carbonate equilibrium"), alpha = 0.5)+
  geom_point(aes(y = pCO2_toc*1e6, col = "pCO2 modelled with TOC"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, uatm")+
  scale_color_manual(values = c("firebrick","dodgerblue"))+
  ylim(0,0.006*1e6)+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

ggarrange(g2,g1, common.legend = T)

Figure 58: pCO2 calculated from TA, compared to pCO2 predicted with TOC, for the NLS surveys

ggplot(nlss)+
  geom_errorbar(aes(x = TOC_mg, ymin = (pCO2_toc - pCO2_toc.se)*1e6, ymax = (pCO2_toc + pCO2_toc.se)*1e6), col = "grey80")+
  geom_point(aes(x = TOC_mg, y = pCO2_toc*1e6), col = "firebrick", size = 0.2)+
  geom_hline(yintercept = fCO2.atm.1995*1e6, col = "pink")+
  theme_bw()

Figure 59: pCO2 calculated from TOC, with sd

ggarrange(
ggplot()+
  geom_point(data = nlss, aes(x = pH, y = pCO2_toc*1e6), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995*1e6, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, uatm", title = "pCO2 predicted from TOC for the Northern European Lakes Survey")+
  scale_color_manual(values = c("firebrick","dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top"),

ggplot()+
  geom_point(data = nlss, aes(x = TA*1e3, y = pCO2_toc*1e6), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995*1e6, lty = 2)+
  labs(x = "TA, eq/L", col = "", y = "pCO2, uatm", title = "pCO2 predicted from TOC for the Northern European Lakes Survey")+
  scale_color_manual(values = c("firebrick","dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top"),
nrow = 2, labels = "AUTO"
)

Figure 60: pCO2 values calculated from TOC for the Northern European Lakes Survey, depending on pH (A) and TA (B)

nlss5.4 <- subset(nlss, pH > 5.4)
knitr::kable(data.frame("Correlation coefficient" = c("Pearson","Spearman"), 
                        "Full dataset" = c(cor(nlss$pCO2_ta, nlss$pCO2_toc, use = "pairwise.complete"),
                                       cor(nlss$pCO2_ta, nlss$pCO2_toc, use = "pairwise.complete", method = "spearman")),
                        "pH > 5.4" = c(cor(nlss5.4$pCO2_ta, nlss5.4$pCO2_toc, use = "pairwise.complete"),
                                       cor(nlss5.4$pCO2_ta, nlss5.4$pCO2_toc, use = "pairwise.complete", method = "spearman"))
                        ),
             digits = 2, col.names = c("Correlation coefficient","Full dataset", "pH > 5.4"), caption = tab_nums("cor-nlss", "Correlation coefficients between pCO2 predicted from TOC and pCO2 calculated from TA for the Northern European Lakes Survey")) %>%
  kable_styling(bootstrap_options = "bordered")

ggplot(nlss)+geom_point(aes(x=long, y = lat, col = pCO2_toc*1e6))+
  borders(regions = c("Norway","Sweden","Finland"))+ylim(55,72)+xlim(4,32)+
  scale_fill_continuous_divergingx(palette = "RdYlBu", aesthetics = c("fill","col"), mid = 1000, rev = T)+
  labs(col="pCO2, uatm")+
  theme_void()

Figure 61: Map of pCO2 values calculated from TOC for the Northern European Lakes Survey

4.2 Boxplots

g1 <- ggplot()+geom_boxplot(data = nlss, aes(x="TA\nNorthern European\nLakes Survey, 1995", y=TA, col = "NLS_1995"))+
  geom_boxplot(data = norway, aes(x = "TA\n CBA (2019) and\nN112 (2004) surveys", y = TA, col = survey))+
  scale_color_manual(values = c("firebrick","orange","dodgerblue"))+
  labs(x = "", col = "",y = "Total alkalinity, eq/L")+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

g2 <- ggplot()+geom_boxplot(data = nlss, aes(x="TOC\nNorthern European\nLakes Survey, 1995", y=TOC_mg, col = "NLS_1995"))+
  geom_boxplot(data = norway, aes(x = "TOC\n CBA (2019) and\nN112 (2004) surveys", y = TOC_mg, col = survey))+
  scale_color_manual(values = c("firebrick","orange","dodgerblue"))+
  labs(x = "", col = "",y = "Total organic carbon, mg/L")+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

g3 <- ggplot()+geom_boxplot(data = nlss, aes(x="pH\nNorthern European\nLakes Survey, 1995", y=pH, col = "NLS_1995"))+
  geom_boxplot(data = norway, aes(x = "pH\n CBA (2019) and\nN112 (2004) surveys", y = pH, col = survey))+
  scale_color_manual(values = c("firebrick","orange","dodgerblue"))+
  labs(x = "", col = "",y = "pH")+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

g4 <- ggplot()+
#    geom_boxplot(data = filter(nlss, pH > 5.4), aes(x="pCO2 TA\nNorthern Europeann\Lakes Survey, 1995", y=pCO2_ta, col = "NLS_1995"))+
  geom_boxplot(data = norway, aes(x = "pCO2\n CBA (2019) and\nN112 (2004) surveys", y = fCO2*1e6, col = survey))+
  geom_boxplot(data = nlss, aes(x="pCO2 TOC\nNorthern European\nLakes Survey, 1995", y=pCO2_toc*1e6, col = "NLS_1995"))+
  scale_color_manual(values = c("firebrick","orange","dodgerblue"))+
  labs(x = "", col = "",y = "pCO2, uatm")+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

ggarrange(g1,g2,g3,g4, common.legend = T, nrow = 2, ncol = 2)

Figure 62: Comparison of the distribution of TA, TOC, pH and pCO2 (measured or predicted) in the CBA, N112 and NLS surveys

5 Evasion rate of CO2

5.1 Theory

Wind speed https://wcrp-cmip.github.io/CMIP6_CVs/docs/CMIP6_institution_id.html

Data downloaded from Copernicus https://cds.climate.copernicus.eu/cdsapp#!/dataset/derived-near-surface-meteorological-variables?tab=overview

See part 1

Theory from Hastie et al. (2018)

\[FCO_2 = A_{lake} \times k \times \Delta CO_2\]

\(FCO_2\) in mol/day, \(A_{lake}\) = lake area in m2, \(\Delta CO_2\) in mol/m3 is the difference between water and air pCO2.

According to Vachon and Prairie (2013):

\[k_{600} = 2.51 + 1.48 \times U_{10} + 0.39 \times U_{10} \times log_{10} (A_{lake})\]

with \(k_600\) in \(cm/h\), \(A\) in km2 and \(U_{10}\) in m/s

Another widely used equation for k600 was introduced by Cole and Caraco (1998) and only uses the wind speed:

\[ k_{600} = 2.07 + 0.215 \times U_{10}^{1.7}\]

\(k_{CO_2}\) has to be adjusted for temperature (Crusius and Wanninkhof 2003) via the Schmidt number:

\[k_{600} = k_{CO_2}\times \left( \frac{600}{Sc_{CO_2}} \right) ^{-n}\]

The Schmidt \(Sc_{CO_2}\) number is calculated from Wanninkhof (2014):

\[S_c = 1923.6 - 125.06 \times T + 4.3773 \times T^2 - 0.085681 \times T^3\]

5.2 Compute ECO2

We calculate the gas transfer coefficient kCO2, based on the normalised gas transfer coefficient k600 and the Schmidt number.

5.2.1 ECO2 for CBA and N112 surveys

norway$pCO2_pred <- fitted(pco2.toc)
norway$pCO2_pred_res <- residuals(pco2.toc)

norway$Sc <- with(norway, 1923.6-125.06*temp_c+4.3733*temp_c^2-0.086781*temp_c^3) #@wanningkhof

norway$n <- NA
for(i in 1:length(norway$n)){
  if(norway$nws_m.s[i] < 3.7 & is.na(norway$nws_m.s[i]) == F){
    norway$n[i] = 2/3
  }else if(norway$nws_m.s[i] > 3.7 & is.na(norway$nws_m.s[i]) == F){
    norway$n[i] = 1/2
  } else if(is.na(norway$nws_m.s[i]) == T){
    norway$n[i] = NA
  }
} # adjusted n from Vachon


norway$k600 <- with(norway, 2.51+1.48*nws_m.s+0.39*nws_m.s*log10(lake.area)) # lake.area already in km2, in cm/h
                    
norway$kCO2 <- with(norway, k600*(600/Sc)^(n))*24*1e-2 # from cm/h to m/day

norway$k600_low <- with(norway, 2.07+0.25*nws_m.s^1.7) # lake area in km2. Cole & Caraco 1998
                    
norway$kCO2_low <- with(norway, k600_low*(600/Sc)^(n))*24*1e-2

norway$ECO2 <- with(norway, kCO2*(fCO2-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

norway$ECO2_low <- with(norway, kCO2_low*(fCO2-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

norway$ECO2_toc <- with(norway, kCO2*(pCO2_pred-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

norway$ECO2_toc_low <- with(norway, kCO2_low*(pCO2_pred-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day


norway$ECO2_ta <- with(norway, kCO2*(ta_fCO2-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

norway$ECO2_ta_low <- with(norway, kCO2_low*(ta_fCO2-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

5.2.2 ECO2 for Northern European Lakes Survey

nlss$Sc <- with(nlss, 1923.6-125.06*temp_c+4.3733*temp_c^2-0.086781*temp_c^3) #@wanningkhof

nlss$n <- NA
for(i in 1:length(nlss$n)){
  if(nlss$nws_m.s[i] < 3.7 & is.na(nlss$nws_m.s[i]) == F){
    nlss$n[i] = 2/3
  }else if(nlss$nws_m.s[i] > 3.7 & is.na(nlss$nws_m.s[i]) == F){
    nlss$n[i] = 1/2
  } else if(is.na(nlss$nws_m.s[i]) == T){
    nlss$n[i] = NA
  }
}


nlss$k600 <- with(nlss, 2.51+1.48*nws_m.s+0.39*nws_m.s*log10(lake.area)) # lake area in km2
                    
nlss$kCO2 <- with(nlss, k600*(600/Sc)^(n))*24*1e-2

nlss$k600_low <- with(nlss, 2.07+0.25*nws_m.s^1.7) # lake area in km2. Cole & Caraco 1998
nlss$kCO2_low <- with(nlss, k600_low*(600/Sc)^(n))*24*1e-2

nlss$ECO2_toc <- with(nlss, kCO2*(pCO2_toc-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day
nlss$ECO2_toc_low <- with(nlss, kCO2_low*(pCO2_toc-fCO2.atm)*K0*1e3 * 12.011)

nlss$ECO2_ta <- with(nlss, kCO2*(pCO2_ta-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day
nlss$ECO2_ta_low <- with(nlss, kCO2_low*(pCO2_ta-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

Figure 63: Median of pCO2 and ECO2, pCO2 calculated from TA (excluding samples with pH < 5.4)

5.2.3 Comparison k600 depending on the method

ggarrange(
  
ggplot()+ geom_boxplot(data=norway, aes(x = survey, y = k600_low, fill = "Cole & Caraco"), position = "dodge2") +
  geom_boxplot(data=nlss, aes(x = "NLSS", y = k600_low, fill = "Cole & Caraco", position = "dodge"))+
  scale_fill_manual(values = "dodgerblue3")+
  ylim(2,21)+
  labs(fill = "", y = "k600 in cm/h", x = "", title = "Cole & Caraco")+
  theme_minimal()+theme(legend.position = "none"),
  
ggplot()+geom_boxplot(data=norway, aes(x = survey, y = k600, fill = "Vachon & Prairie", position = "dodge2"))+
   geom_boxplot(data=nlss, aes(x = "NLSS", y = k600, fill = "Vachon & Prairie"))+
  scale_fill_manual(values = "firebrick")+
  ylim(2,21)+
  labs(fill = "", y = "k600 in cm/h", x = "", title = "Vachon & Prairie")+
  theme_minimal()+theme(legend.position = "none"),

common.legend = F, align = "hv"

)

Figure 64: Boxplots of the k600 calculated for each survey, low estimate (Cole & Caraco) and high estimate (Vachon & Prairie))

ggplot(norway, aes(x = lake.area)) + geom_point(aes(y = k600, col = "Vachon and Prairie"))+
          geom_point(aes(y = k600_low, col = "Cole and Caraco")) + 
          coord_trans(x = "log10") + 
          labs(x = "Lake area in km2")+
          scale_x_continuous(breaks = c(0.1, 0.5,1,2.5, 5,10,25,50, 100, 250), minor_breaks = NULL)+
          scale_color_manual(values = c("dodgerblue3","firebrick"))+
          theme_bw()

ggplot(nlss, aes(x = lake.area)) + 
          geom_point(aes(y = ECO2_toc, col = "Vachon and Prairie (including lake area)"), alpha = 0.5)+
          geom_point(aes(y = ECO2_toc_low, col = "Cole and Caraco (without lake area)"), alpha = 0.5) + 
          scale_color_manual(values = c("dodgerblue3","firebrick"))+
          labs(x = "Lare area in km2", y = "ECO2 in gC/m/day", col = "k600 calculated with")+
          coord_trans(x = "log10") + 
          scale_x_continuous(breaks = c(0.1, 0.5,1,2.5, 5,10,25,50, 100, 250), minor_breaks = NULL)+
          theme_bw() +
          theme(legend.position = "bottom")

Figure 65: Calculated ECO2 depending on lake area (log-scale) with low estimate of k600 (in blue, without lake area) and red (including lake area)

5.3 Compare ECO2 from TOC and ECO2 from TA

Comparison of the ECO2 obtained by calculation pCO2 from TOC or TA (in that case, we remove samples in which pH < 5.4).

Table 3: Median of pCO2 and ECO2, pCO2 predicted from TOC

no <- norway %>% 
  dplyr::select(c("survey", "fCO2" ,"pCO2_pred", "ECO2_toc", "ECO2_toc_low")) %>% 
  mutate(nation = "Norway") %>% 
  setNames(c("survey","measured_pCO2","pCO2_toc","ECO2_high","ECO2_low","nation"))  %>% 
  dplyr::select(c("survey","nation","measured_pCO2","pCO2_toc","ECO2_high","ECO2_low"))

fns <- nlss %>% as_data_frame() %>%
  dplyr::select(c("nation", "pCO2_toc", "ECO2_toc", "ECO2_toc_low")) %>% 
  mutate(fCO2 = NA, survey = "nls_1995") %>% 
  setNames(c("nation","pCO2_toc","ECO2_high", "ECO2_low","measured_pCO2","survey")) %>% 
  dplyr::select(c("survey","nation","measured_pCO2","pCO2_toc","ECO2_high","ECO2_low"))

summary_eco2 <- rbind(no,fns) %>% group_by(nation, survey) %>% summarize_all(median, na.rm = T) 
kable(summary_eco2) %>% kable_styling()

nation	survey	measured_pCO2	pCO2_toc	ECO2_high	ECO2_low
Finland	nls_1995		0.0010432	0.6452481	0.3917249
Norway	CBA_2019	0.0011346	0.0015690	0.8252406	0.4543466
Norway	N112_2004	0.0006845	0.0006680	0.2287118	0.1213060
Norway	nls_1995		0.0005835	0.1127527	0.0659726
Sweden	nls_1995		0.0009819	0.5745514	0.3606773

Table 4: Median of pCO2 and ECO2, pCO2 calculated from TA (excluding samples with pH < 5.4)

ggarrange(
  plotlist = list(
ggplot(subset(norway, survey == "CBA_2019"))+geom_density(aes(x = ECO2, fill = "High estimate, measured"), alpha = 0.3, col = NA)+
  geom_density(aes(x=ECO2_toc, fill = "High estimate, TOC"), alpha = 0.3, col = NA) +
  geom_vline(aes(xintercept = median(subset(norway, survey == "CBA_2019")$ECO2), col = "High estimate, measured", linetype = "median"))+
  geom_vline(aes(xintercept = mean(subset(norway, survey == "CBA_2019")$ECO2), col = "High estimate, measured", linetype = "mean"))+
  geom_vline(aes(xintercept = median(subset(norway, survey == "CBA_2019")$ECO2_toc), col = "High estimate, TOC", linetype = "median"))+
  geom_vline(aes(xintercept = mean(subset(norway, survey == "CBA_2019")$ECO2_toc), col = "High estimate, TOC", linetype = "mean"))+
 scale_color_manual(values = c("dodgerblue3","firebrick","dodgerblue3","firebrick"))+
   scale_fill_manual(values = c("dodgerblue3","firebrick"))+
  labs(x = "ECO2 in gC/m2/day", col = "",linetype = "", title = "CBA, 2019", fill = "")+
  theme_minimal()
,
ggplot(subset(norway, survey == "N112_2004"))+geom_density(aes(x = ECO2, fill = "High estimate, measured"), alpha = 0.3, col = NA)+
 geom_density(aes(x=ECO2_toc, fill = "High estimate, TOC"), alpha = 0.3, col = NA) +
  geom_vline(aes(xintercept = median(subset(norway, survey == "N112_2004")$ECO2), col = "High estimate, measured", linetype = "median"))+
  geom_vline(aes(xintercept = mean(subset(norway, survey == "N112_2004")$ECO2), col = "High estimate, measured", linetype = "mean"))+
    geom_vline(aes(xintercept = median(subset(norway, survey == "N112_2004")$ECO2_toc), col = "High estimate, TOC", linetype = "median"))+
  geom_vline(aes(xintercept = mean(subset(norway, survey == "N112_2004")$ECO2_toc), col = "High estimate, TOC", linetype = "mean"))+
  scale_color_manual(values = c("dodgerblue3","firebrick","dodgerblue3","firebrick"))+
   scale_fill_manual(values = c("dodgerblue3","firebrick"))+
  labs(x = "ECO2 in gC/m2/day", col = "", linetype = "", title = "N112, 2004", fill = "")+
  theme_minimal()
),
  common.legend = T, legend = "bottom")

ggarrange(
  plotlist = list(
ggplot(subset(norway, survey == "CBA_2019"))+geom_density(aes(x = ECO2_low, fill = "Low estimate, measured"), alpha = 0.3, col = NA)+
  geom_density(aes(x=ECO2_toc_low, fill = "Low estimate, TOC"), alpha = 0.3, col = NA) +
  geom_vline(aes(xintercept = median(subset(norway, survey == "CBA_2019")$ECO2_low), col = "Low estimate, measured", linetype = "median"))+
  geom_vline(aes(xintercept = mean(subset(norway, survey == "CBA_2019")$ECO2_low), col = "Low estimate, measured", linetype = "mean"))+
  geom_vline(aes(xintercept = median(subset(norway, survey == "CBA_2019")$ECO2_toc_low), col = "Low estimate, TOC", linetype = "median"))+
  geom_vline(aes(xintercept = mean(subset(norway, survey == "CBA_2019")$ECO2_toc_low), col = "Low estimate, TOC", linetype = "mean"))+
 scale_color_manual(values = c("dodgerblue3","firebrick","dodgerblue3","firebrick"))+
   scale_fill_manual(values = c("dodgerblue3","firebrick"))+
  labs(x = "ECO2 in gC/m2/day", col = "",linetype = "", title = "CBA, 2019", fill = "")+
  theme_minimal()
,
ggplot(subset(norway, survey == "N112_2004"))+geom_density(aes(x = ECO2_low, fill = "Low estimate, measured"), alpha = 0.3, col = NA)+
 geom_density(aes(x=ECO2_toc_low, fill = "Low estimate, TOC"), alpha = 0.3, col = NA) +
  geom_vline(aes(xintercept = median(subset(norway, survey == "N112_2004")$ECO2_low), col = "Low estimate, measured", linetype = "median"))+
  geom_vline(aes(xintercept = mean(subset(norway, survey == "N112_2004")$ECO2_low), col = "Low estimate, measured", linetype = "mean"))+
    geom_vline(aes(xintercept = median(subset(norway, survey == "N112_2004")$ECO2_toc_low), col = "Low estimate, TOC", linetype = "median"))+
  geom_vline(aes(xintercept = mean(subset(norway, survey == "N112_2004")$ECO2_toc_low), col = "Low estimate, TOC", linetype = "mean"))+
  scale_color_manual(values = c("dodgerblue3","firebrick","dodgerblue3","firebrick"))+
   scale_fill_manual(values = c("dodgerblue3","firebrick"))+
  labs(x = "ECO2 in gC/m2/day", col = "", linetype = "", title = "N112, 2004", fill = "")+
  theme_minimal()
),
  common.legend = T, legend = "bottom")

Figure 66: Comparison of the distribution of low and high estimates of ECO2 for the CBA and N112 surveys

no <- norway %>% 
  dplyr::select(c("survey", "pH", "fCO2", "ta_fCO2", "ECO2_ta", "ECO2_ta_low")) %>% 
  mutate(nation = "Norway") %>% 
  setNames(c("survey","pH","measured_pCO2","pCO2_ta","ECO2_high","ECO2_low","nation"))  %>%
  dplyr::select(c("survey","nation","pH","measured_pCO2","pCO2_ta","ECO2_high","ECO2_low"))

fns <- nlss %>% as_data_frame() %>%
  dplyr::select(c("nation", "pH","pCO2_ta","ECO2_ta", "ECO2_ta_low")) %>% 
  mutate(fCO2 = NA, survey = "nls_1995") %>% 
  setNames(c("nation","pH","pCO2_ta","ECO2_high", "ECO2_low","measured_pCO2","survey")) %>% 
  dplyr::select(c("survey","nation","pH","measured_pCO2","pCO2_ta","ECO2_high","ECO2_low"))

summary_eco2_ta <- rbind(no,fns) %>% filter(pH > 5.4) %>% group_by(nation, survey) %>% summarize_all(median, na.rm = T) 
kable(summary_eco2_ta) %>% kable_styling()

nation	survey	pH	measured_pCO2	pCO2_ta	ECO2_high	ECO2_low
Finland	nls_1995	6.70		0.0013406	0.8801672	0.5303916
Norway	CBA_2019	6.87	0.0011346	0.0015188	0.6997074	0.3625881
Norway	N112_2004	6.07	0.0006381	0.0009285	0.3790531	0.1897891
Norway	nls_1995	6.54		0.0007590	0.1992923	0.1199373
Sweden	nls_1995	6.85		0.0011476	0.7451497	0.4701856

ggplot(nlss)+geom_point(aes(x=long, y = lat, col = ECO2_toc_low))+
  borders(regions = c("Norway","Sweden","Finland"))+ylim(55,72)+xlim(4,32)+
  scale_fill_continuous_divergingx(palette = "RdYlBu", aesthetics = c("fill","col"), mid = 0.5,rev = T)+
  labs(col="ECO2, gC/m2/day")+
  theme_void()

5.4 Summary table with median and mean, TOC

Table 5: Median and mean of pCO2 and ECO2, pCO2 predicted from TOC, by survey

no <- norway %>% 
  dplyr::select(c("survey", "fCO2" , "ECO2", "ECO2_toc","ECO2_low", "ECO2_toc_low")) 

medyear <- function(x){median(x, na.rm = T) * 365} # to convert gC/m2/d in gC/m2/year
avyear <- function(x){mean(x, na.rm = T) * 365}
sdyear<- function(x){sd(x, na.rm = T) * 365}

summary_no.1 <- no %>% group_by(survey) %>% summarize_all(medyear) %>% mutate(fCO2 = fCO2/365*1e6) #divide fCO2 by 365 to come back to mean concentration value
summary_no.2 <- no %>% group_by(survey) %>% summarize_all(avyear) %>% mutate(fCO2 = fCO2/365*1e6) # + convert to uatm
summary_no.3 <- no %>% group_by(survey) %>% summarize_all(sdyear) %>% mutate(fCO2 = fCO2/365*1e6)

no2 <- rbind(summary_no.1, summary_no.2, summary_no.3) %>% arrange(survey) %>% mutate(survey = c("median","mean","standard deviation","median","mean","standard deviation"))

fen <- nlss %>% dplyr::select(c("pCO2_toc","ECO2_toc","ECO2_toc_low")) %>% 
  mutate(ECO2 = NA, ECO2_low = NA, fCO2 = pCO2_toc/365*1e6, survey = NA) %>%
  dplyr::select(c("survey","fCO2", "ECO2", "ECO2_toc", "ECO2_low","ECO2_toc_low")) 
fen$lake.id <- NULL

summary_fen.1 <- fen %>% group_by(survey) %>% summarize_all(medyear) %>% mutate(survey= "median")
summary_fen.2 <- fen %>% group_by(survey) %>% summarize_all(avyear) %>% mutate(survey= "mean")
summary_fen.3 <- fen %>% group_by(survey) %>% summarize_all(sdyear) %>% mutate(survey= "standard deviation")

tot <- rbind(no2, summary_fen.1) %>% rbind(summary_fen.2) %>% rbind(summary_fen.3)

kable(tot, digits = 2, col.names = c(" ","pCO2, uatm", "ECO2 from DIC in gC/m2/day","ECO2 from TOC in gC/m2/day","ECO2 from DIC in gC/m2/day","ECO2 from TOC in gC/m2/day")) %>% 
  kable_styling %>% 
  kableExtra::group_rows(group_label= "CBA", start_row = 1, end_row = 3) %>%
  kableExtra::group_rows(group_label= "N112", start_row = 4, end_row = 6) %>% 
  kableExtra::group_rows(group_label= "NLS", start_row = 7, end_row = 9) %>% 
  kableExtra::add_header_above(c(" " = 2, "High estimates" = 2, "Low estimates" = 2)) 

		High estimates		Low estimates
	pCO2, uatm	ECO2 from DIC in gC/m2/day	ECO2 from TOC in gC/m2/day	ECO2 from DIC in gC/m2/day	ECO2 from TOC in gC/m2/day
CBA
median	1134.57	183.74	301.21	100.56	165.84
mean	1517.26	264.19	337.36	157.73	184.89
standard deviation	1266.08	302.90	320.95	210.27	149.71
N112
median	684.50	80.27	83.48	46.72	44.28
mean	779.18	109.49	95.35	60.31	51.87
standard deviation	391.00	104.85	86.59	60.49	48.01
NLS
median	929.36		175.38		106.94
mean	998.84		209.77		139.10
standard deviation	448.79		178.76		131.96

# kable(tot, digits = 2, col.names = c(" ","pCO2, uatm", "ECO2 from DIC in gC/m2/year","ECO2 from TOC in gC/m2/year","ECO2 from DIC in gC/m2/year","ECO2 from TOC in gC/m2/year")) %>% 
#   kable_styling() %>% 
#   kableExtra::group_rows(group_label= "CBA", start_row = 1, end_row = 3) %>%
#   kableExtra::group_rows(group_label= "N112", start_row = 4, end_row = 6) %>%
#   kableExtra::group_rows(group_label= "NLS", start_row = 7, end_row = 9) %>% 
#   kableExtra::add_header_above(c(" " = 2, "High estimates" = 2, "Low estimates" = 2)) %>%
#   save_kable(file = "compare.eco2.measured.png",zoom = 5)

5.5 Compare total emissions calculated from bins, with total emissions calculated from median and mean

We also compare with the efflux calculated by Hastie et al. (2018) by class of area. The efflux is given in TgC/year. We convert it to gC/m2/year for each country.

Table 6: Total efflux of CO2 computed from the median for each lake category, compared to efflux calculated for all lakes (Norway, Sweden, Finland)

options(knitr.kable.NA = '')

p0 <- median(nlss$pCO2_toc, na.rm = T)*1e6
A0 <- sum(nlss$lake.area)
k0 <- nlss$kCO2 %>% median(na.rm = T) 
k0_low <- nlss$kCO2_low %>% median(na.rm = T)
E0 <- median(nlss$ECO2_toc * 365, na.rm = T) # gC/m2/y
E0_low <- median(nlss$ECO2_toc_low * 365, na.rm = T) # gC/m2/y

F0_realsum <-  with(nlss, sum(ECO2_toc * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F0_sumfrommedian <- with(nlss, E0*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

F0_low_realsum <-  with(nlss, sum(ECO2_toc_low * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F0_low_sumfrommedian <- with(nlss, E0_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

# Lake size < 0.1 km2

p1 <- nlss %>% subset(lake.area < 0.1) %>% pull(pCO2_toc) %>% median()*1e6
A1 <- nlss %>% subset(lake.area < 0.1) %>% pull(lake.area) %>% sum()

k1 <- with(subset(nlss, lake.area < 0.1), median(kCO2, na.rm = T)) 
E1 <- with(subset(nlss, lake.area < 0.1), median(ECO2_toc*365, na.rm = T)) #gC/m2/y

F1_realsum <- with(subset(nlss, lake.area < 0.1), sum(ECO2_toc * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F1_sumfrombin <- with(subset(nlss, lake.area < 0.1), E1*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

  
k1_low <- with(subset(nlss, lake.area < 0.1), median(kCO2_low, na.rm = T)) 
E1_low <- with(subset(nlss, lake.area < 0.1), median(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F1_low_realsum <- with(subset(nlss, lake.area < 0.1), sum(ECO2_toc_low * 365/12.011 * 43.99  * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F1_low_sumfrombin <- with(subset(nlss, lake.area < 0.1), E1_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


W1 <- 38.17*1e12/(208008*1e6) # gC/m2/year in Weyhenmeyer
W1_sum <- with(subset(nlss, lake.area < 0.1), W1*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 0.1 < Lake size < 1 km2

p2 <- nlss %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(pCO2_toc) %>% median()*1e6
A2 <- nlss %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(lake.area) %>% sum()

k2 <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), median(kCO2, na.rm = T)) 
E2 <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), median(ECO2_toc*365, na.rm = T)) #gC/m2/y

F2_realsum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), sum(ECO2_toc * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F2_sumfrombin <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), E2*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


k2_low <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), median(kCO2_low, na.rm = T)) 
E2_low <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), median(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F2_low_realsum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), sum(ECO2_toc_low * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F2_low_sumfrombin <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), E2_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)



W2 <- 52.36*1e12/(282434*1e6) # gC/m2/year in W
W2_sum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), W2*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 1 < Lake size < 10 km2

p3 <- nlss %>% subset(lake.area > 1 & lake.area < 10) %>% pull(pCO2_toc) %>% median()*1e6
A3 <- nlss %>% subset(lake.area > 1 & lake.area < 10) %>% pull(lake.area) %>% sum()

k3 <- with(subset(nlss, lake.area > 1 & lake.area < 10), median(kCO2, na.rm = T)) 
E3 <- with(subset(nlss, lake.area > 1 & lake.area < 10), median(ECO2_toc*365, na.rm = T)) #gC/m2/y

F3_realsum <- with(subset(nlss, lake.area > 1 & lake.area < 10), sum(ECO2_toc * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F3_sumfrombin <- with(subset(nlss, lake.area > 1 & lake.area < 10), E3*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


k3_low <- with(subset(nlss, lake.area > 1 & lake.area < 10), median(kCO2_low, na.rm = T)) 
E3_low <- with(subset(nlss, lake.area > 1 & lake.area < 10), median(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F3_low_realsum <- with(subset(nlss, lake.area > 1 & lake.area < 10), sum(ECO2_toc_low * 365/12.011 * 43.99  * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F3_low_sumfrombin <- with(subset(nlss, lake.area > 1 & lake.area < 10), E3_low*sum(lake.area*1e6)/12.011 * 43.99  * 1e-12)


W3 <- 22.80*1e12/(286624*1e6) # gC/m2/year in W
W3_sum <- with(subset(nlss, lake.area > 1 & lake.area < 10), W3*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 1 < Lake size < 10 km2

p4 <- nlss %>% subset(lake.area > 10) %>% pull(pCO2_toc) %>% median()*1e6
A4 <- nlss %>% subset(lake.area > 10) %>% pull(lake.area) %>% sum()

k600_4 <- with(subset(nlss, lake.area > 10), median(k600*24*1e-2, na.rm = T))
k600_4_low <- with(subset(nlss, lake.area > 10), median(k600_low*24*1e-2, na.rm = T))

k4 <- with(subset(nlss, lake.area > 10), median(kCO2, na.rm = T)) 
E4 <- with(subset(nlss, lake.area > 10), median(ECO2_toc*365, na.rm = T)) #gC/m2/y

F4_realsum <- with(subset(nlss, lake.area > 10), sum(ECO2_toc* 365*lake.area*1e6/12.011 * 43.99  * 1e-12, na.rm = T)) #MtCO2/y
F4_sumfrombin <- with(subset(nlss, lake.area > 10), E4*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)



k4_low <- with(subset(nlss, lake.area > 10), median(kCO2_low, na.rm = T)) 
E4_low <- with(subset(nlss, lake.area > 10), median(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F4_low_realsum <- with(subset(nlss, lake.area > 10), sum(ECO2_toc_low* 365*lake.area*1e6/12.011 * 43.99  * 1e-12, na.rm = T)) #MtCO2/y
F4_low_sumfrombin <- with(subset(nlss, lake.area > 10), E4_low*sum(lake.area*1e6)/12.011 * 43.99  * 1e-12)


W4 <- 53.96*1e12/(570583*1e6) # gC/m2/year in W
W4_sum <- with(subset(nlss, lake.area > 10), W4*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

bin_FCO2 <- data.frame(lake.size = c("A < 0.1","0.1 < A < 1","1 < A < 10","> 10","sum"," "), 
          lake.area = c(A1, A2, A3, A4, NA,A0),
           pCO2 = c(p1,p2,p3,p4,NA,p0), 
           kCO2_low = c(k1_low,k2_low,k3_low,k4_low,NA,k0_low), 
           E_low = c(E1_low,E2_low,E3_low,E4_low,NA,E0_low),
           FCO2_low_bin = c(F1_low_sumfrombin, F2_low_sumfrombin, F3_low_sumfrombin, F4_low_sumfrombin, sum(F1_low_sumfrombin, F2_low_sumfrombin, F3_low_sumfrombin, F4_low_sumfrombin),F0_low_sumfrommedian),
            FCO2_low = c(F1_low_realsum, F2_low_realsum, F3_low_realsum, F4_low_realsum,sum(F1_low_realsum,F2_low_realsum,F3_low_realsum,F4_low_realsum),F0_low_realsum),
           kCO2_high = c(k1,k2,k3,k4, NA,k0),
           E_high = c(E1,E2,E3,E4, NA,E0),
           FCO2_high_bin = c(F1_sumfrombin, F2_sumfrombin, F3_sumfrombin, F4_sumfrombin, sum(F1_sumfrombin, F2_sumfrombin, F3_sumfrombin, F4_sumfrombin),F0_sumfrommedian),
          FCO2_high = c(F1_realsum, F2_realsum, F3_realsum, F4_realsum, sum(F1_realsum, F2_realsum, F3_realsum, F4_realsum),F0_realsum),
           Wey = c(W1,W2,W3,W4, NA,NA),
           Wey_sum = c(W1_sum, W2_sum, W3_sum, W4_sum, sum(W1_sum, W2_sum, W3_sum, W4_sum),NA))


kable(bin_FCO2, digits = 2, col.names = c("A = lake area in km2","Total lake area in km2","median pCO2, uatm","median kCO2, m2/d","median ECO2, g/m2/y", "binned FCO2, MtCO2/y","actual FCO2, MtCO2/y","kCO2, m2/d","median ECO2, g/m2/y", "binned FCO2, MtCO2/y", "actual FCO2, MtCO2/y","median ECO2, g/m2/day", "FCO2, MtCO2/y")) %>% kable_styling() %>% 
  kableExtra::add_header_above(c("Lake class" = 2, " " = 1, "Low estimate" = 4, "High estimate" = 4, "Hastie et al." = 2)) %>%
  kableExtra::group_rows(group_label= "All lakes", start_row = 6, end_row = 6) %>%
  column_spec(column = c(5,6,9,10,12), bold = T)

Lake class			Low estimate				High estimate				Hastie et al.
A = lake area in km2	Total lake area in km2	median pCO2, uatm	median kCO2, m2/d	median ECO2, g/m2/y	binned FCO2, MtCO2/y	actual FCO2, MtCO2/y	kCO2, m2/d	median ECO2, g/m2/y	binned FCO2, MtCO2/y	actual FCO2, MtCO2/y	median ECO2, g/m2/day	FCO2, MtCO2/y
A < 0.1	89.23	946.87	0.55	91.89	0.03	0.05	0.78	131.26	0.04	0.06	183.50	0.06
0.1 < A < 1	449.17	955.63	0.73	120.00	0.20	0.23	1.14	188.26	0.31	0.37	185.39	0.30
1 < A < 10	2386.51	911.84	0.78	113.96	1.00	1.13	1.44	213.85	1.87	2.10	79.55	0.70
> 10	32393.63	872.44	0.66	98.68	11.71	14.08	1.57	234.54	27.83	36.60	94.57	11.22
sum					12.93	15.49			30.05	39.14		12.28
All lakes
	35318.55	929.36	0.64	106.94	13.83	15.49	1.03	175.38	22.69	39.14

Table 7: Total efflux of CO2 computed from the mean for each lake category, compared to efflux calculated for all lakes (Norway, Sweden, Finland)

p0 <- mean(nlss$pCO2_toc, na.rm = T)*1e6
A0 <- sum(nlss$ake.area)
k0 <- nlss$kCO2 %>% mean(na.rm = T) 
k0_low <- nlss$kCO2_low %>% mean(na.rm = T)
E0 <- mean(nlss$ECO2_toc * 365, na.rm = T) # gC/m2/y
E0_low <- mean(nlss$ECO2_toc_low * 365, na.rm = T) # gC/m2/y

F0_realsum <-  with(nlss, sum(ECO2_toc * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F0_sumfrommean <- with(nlss, E0*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

F0_low_realsum <-  with(nlss, sum(ECO2_toc_low * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F0_low_sumfrommean <- with(nlss, E0_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

# Lake size < 0.1 km2

p1 <- nlss %>% subset(lake.area < 0.1) %>% pull(pCO2_toc) %>% mean()*1e6
A1 <- nlss %>% subset(lake.area < 0.1) %>% pull(lake.area) %>% sum()

k1 <- with(subset(nlss, lake.area < 0.1), mean(kCO2, na.rm = T)) 
E1 <- with(subset(nlss, lake.area < 0.1), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y

F1_realsum <- with(subset(nlss, lake.area < 0.1), sum(ECO2_toc * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F1_sumfrombin <- with(subset(nlss, lake.area < 0.1), E1*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

  
k1_low <- with(subset(nlss, lake.area < 0.1), mean(kCO2_low, na.rm = T)) 
E1_low <- with(subset(nlss, lake.area < 0.1), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F1_low_realsum <- with(subset(nlss, lake.area < 0.1), sum(ECO2_toc_low * 365/12.011 * 43.99  * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F1_low_sumfrombin <- with(subset(nlss, lake.area < 0.1), E1_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


W1 <- 38.17*1e12/(208008*1e6) # gC/m2/year in Weyhenmeyer
W1_sum <- with(subset(nlss, lake.area < 0.1), W1*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 0.1 < Lake size < 1 km2

p2 <- nlss %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(pCO2_toc) %>% mean()*1e6

k2 <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), mean(kCO2, na.rm = T)) 
E2 <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y

F2_realsum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), sum(ECO2_toc * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F2_sumfrombin <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), E2*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


k2_low <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), mean(kCO2_low, na.rm = T)) 
E2_low <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F2_low_realsum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), sum(ECO2_toc_low * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F2_low_sumfrombin <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), E2_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)



W2 <- 52.36*1e12/(282434*1e6) # gC/m2/year in W
W2_sum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), W2*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 1 < Lake size < 10 km2

p3 <- nlss %>% subset(lake.area > 1 & lake.area < 10) %>% pull(pCO2_toc) %>% mean()*1e6

k3 <- with(subset(nlss, lake.area > 1 & lake.area < 10), mean(kCO2, na.rm = T)) 
E3 <- with(subset(nlss, lake.area > 1 & lake.area < 10), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y

F3_realsum <- with(subset(nlss, lake.area > 1 & lake.area < 10), sum(ECO2_toc * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F3_sumfrombin <- with(subset(nlss, lake.area > 1 & lake.area < 10), E3*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


k3_low <- with(subset(nlss, lake.area > 1 & lake.area < 10), mean(kCO2_low, na.rm = T)) 
E3_low <- with(subset(nlss, lake.area > 1 & lake.area < 10), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F3_low_realsum <- with(subset(nlss, lake.area > 1 & lake.area < 10), sum(ECO2_toc_low * 365/12.011 * 43.99  * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F3_low_sumfrombin <- with(subset(nlss, lake.area > 1 & lake.area < 10), E3_low*sum(lake.area*1e6)/12.011 * 43.99  * 1e-12)


W3 <- 22.80*1e12/(286624*1e6) # gC/m2/year in W
W3_sum <- with(subset(nlss, lake.area > 1 & lake.area < 10), W3*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 1 < Lake size < 10 km2

p4 <- nlss %>% subset(lake.area > 10) %>% pull(pCO2_toc) %>% mean()*1e6

k600_4 <- with(subset(nlss, lake.area > 10), mean(k600*24*1e-2, na.rm = T))
k600_4_low <- with(subset(nlss, lake.area > 10), mean(k600_low*24*1e-2, na.rm = T))

k4 <- with(subset(nlss, lake.area > 10), mean(kCO2, na.rm = T)) 
E4 <- with(subset(nlss, lake.area > 10), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y

F4_realsum <- with(subset(nlss, lake.area > 10), sum(ECO2_toc* 365*lake.area*1e6/12.011 * 43.99  * 1e-12, na.rm = T)) #MtCO2/y
F4_sumfrombin <- with(subset(nlss, lake.area > 10), E4*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)



k4_low <- with(subset(nlss, lake.area > 10), mean(kCO2_low, na.rm = T)) 
E4_low <- with(subset(nlss, lake.area > 10), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F4_low_realsum <- with(subset(nlss, lake.area > 10), sum(ECO2_toc_low* 365*lake.area*1e6/12.011 * 43.99  * 1e-12, na.rm = T)) #MtCO2/y
F4_low_sumfrombin <- with(subset(nlss, lake.area > 10), E4_low*sum(lake.area*1e6)/12.011 * 43.99  * 1e-12)


W4 <- 53.96*1e12/(570583*1e6) # gC/m2/year in W
W4_sum <- with(subset(nlss, lake.area > 10), W4*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

bin_FCO2 <- data.frame(lake.size = c("A < 0.1","0.1 < A < 1","1 < A < 10","> 10","sum"," "), 
           pCO2 = c(p1,p2,p3,p4,NA,p0), 
           kCO2_low = c(k1_low,k2_low,k3_low,k4_low,NA,k0_low), 
           E_low = c(E1_low,E2_low,E3_low,E4_low,NA,E0_low),
           FCO2_low_bin = c(F1_low_sumfrombin, F2_low_sumfrombin, F3_low_sumfrombin, F4_low_sumfrombin, sum(F1_low_sumfrombin, F2_low_sumfrombin, F3_low_sumfrombin, F4_low_sumfrombin),F0_low_sumfrommean),
            FCO2_low = c(F1_low_realsum, F2_low_realsum, F3_low_realsum, F4_low_realsum,sum(F1_low_realsum,F2_low_realsum,F3_low_realsum,F4_low_realsum),F0_low_realsum),
           kCO2_high = c(k1,k2,k3,k4, NA,k0),
           E_high = c(E1,E2,E3,E4, NA,E0),
           FCO2_high_bin = c(F1_sumfrombin, F2_sumfrombin, F3_sumfrombin, F4_sumfrombin, sum(F1_sumfrombin, F2_sumfrombin, F3_sumfrombin, F4_sumfrombin),F0_sumfrommean),
          FCO2_high = c(F1_realsum, F2_realsum, F3_realsum, F4_realsum, sum(F1_realsum, F2_realsum, F3_realsum, F4_realsum),F0_realsum),
           Wey = c(W1,W2,W3,W4, NA,NA),
           Wey_sum = c(W1_sum, W2_sum, W3_sum, W4_sum, sum(W1_sum, W2_sum, W3_sum, W4_sum),NA))


kable(bin_FCO2, digits = 2, col.names = c("A = lake area in km2","mean pCO2, uatm","mean kCO2, m2/d","mean ECO2, g/m2/y", "binned FCO2, MtCO2/y","actual FCO2, MtCO2/y","kCO2, m2/d","mean ECO2, g/m2/y", "binned FCO2, MtCO2/y", "actual FCO2, MtCO2/y","mean ECO2, g/m2/day", "FCO2, MtCO2/y")) %>% kable_styling() %>% 
  kableExtra::add_header_above(c("Lake class" = 1, " " = 1, "Low estimate" = 4, "High estimate" = 4, "Hastie et al." = 2)) %>%
  kableExtra::group_rows(group_label= "All lakes", start_row = 6, end_row = 6) %>%
  column_spec(column = c(5,6,9,10,12), bold = T)

Lake class		Low estimate				High estimate				Hastie et al.
A = lake area in km2	mean pCO2, uatm	mean kCO2, m2/d	mean ECO2, g/m2/y	binned FCO2, MtCO2/y	actual FCO2, MtCO2/y	kCO2, m2/d	mean ECO2, g/m2/y	binned FCO2, MtCO2/y	actual FCO2, MtCO2/y	mean ECO2, g/m2/day	FCO2, MtCO2/y
A < 0.1	1034.90	0.64	142.24	0.05	0.05	0.85	183.69	0.06	0.06	183.50	0.06
0.1 < A < 1	1019.58	0.71	146.78	0.24	0.23	1.10	220.73	0.36	0.37	185.39	0.30
1 < A < 10	939.33	0.74	130.85	1.14	1.13	1.35	234.94	2.05	2.10	79.55	0.70
> 10	860.24	0.73	106.64	12.65	14.08	1.63	234.97	27.88	36.60	94.57	11.22
sum				14.08	15.49			30.35	39.14		12.28
All lakes
	998.84	0.69	139.10	17.99	15.49	1.09	209.77	27.13	39.14

5.6 Bin estimation by country for all inland waters

We estimated the share of inland waters belonging to a given category of lakes (depending on area in km2) based on the proportion represented by each category in the total of the lakes sampled during the Northern European Lakes Survey.

The largest lakes of Norway, Sweden and Finland account for a large part of the total inland waters. Therefore, we included them as a separated category. We assumed that all the lakes with an area larger than 100 km2 were sampled in the NLS. Therefore, the CO2 efflux for these big lakes were simply added to the efflux calculated for the rest of the inland water.

ggplot(nlss)+geom_boxplot(aes(x=nation, y = lake.area, col = nation))+coord_trans(y = "log10")+
  scale_color_manual(values = c("firebrick","orange","dodgerblue3"))+
  geom_hline(yintercept = 100)+
  labs(y = "Lake area, km2", x = "")+
  scale_y_continuous(breaks = c(0.1,1,10,100))+
  theme_minimal()

Table 8: Total efflux of CO2 computed from the mean for each lake category, compared to efflux calculated for all lakes in Norway

CAN BE RECODED WITH AN EXTRA COLUMN INDICATING LAKE CATEGORY + summarise That would help for calculating uncertainty on each resulting number

breaks.lakes <- c(0,0.1,1,10,100,Inf)

nlss$lake.category <- cut(nlss$lake.area, breaks.lakes)

nlss$inland.water <- NA
nlss$inland.water[which(nlss$nation == "Norway")] <- 20221  # km2 , @SSB
nlss$inland.water[which(nlss$nation == "Sweden")] <- 4014169.92 * 1e-2 # ha to km2, @SCB
nlss$inland.water[which(nlss$nation == "Finland")] <- 34515 # km2, @Statfi

nlss$lake.area.under100 <- NA
nlss$lake.area.under100[which(nlss$nation == "Norway")] <- sum(subset(nlss, nation == "Norway" & lake.area < 100)$lake.area) # nlss area without biggest lakes
nlss$lake.area.under100[which(nlss$nation == "Sweden")] <- sum(subset(nlss, nation == "Sweden" & lake.area < 100)$lake.area)# nlss area without biggest lakes
nlss$lake.area.under100[which(nlss$nation == "Finland")] <- sum(subset(nlss, nation == "Finland" & lake.area < 100)$lake.area) # nlss area without biggest lakes

nlss$lake.area.over100 <- NA
nlss$lake.area.over100[which(nlss$nation == "Norway")] <- sum(subset(nlss, nation == "Norway" & lake.area > 100)$lake.area) # areas of biggest lakes
nlss$lake.area.over100[which(nlss$nation == "Sweden")] <- sum(subset(nlss, nation == "Sweden" & lake.area > 100)$lake.area) # areas of biggest lakes
nlss$lake.area.over100[which(nlss$nation == "Finland")] <- sum(subset(nlss, nation == "Finland" & lake.area > 100)$lake.area) # areas of biggest lakes

binned.nlss <- nlss %>% group_by(nation, inland.water, lake.area.under100, lake.area.over100, lake.category) %>% 
                        summarise(nb.lakes = n(),
                                  cat.lake.area = sum(lake.area),
                                  prop.cat = ifelse(lake.category != "(100,Inf]", cat.lake.area/lake.area.under100 * 100, NA),
                                  pCO2 = mean(pCO2_toc * 1e6, na.rm = T),  # in uatm
                                  pCO2_sd = sd(pCO2_toc * 1e6, na.rm = T),
                                  kCO2_mean = mean(kCO2, na.rm = T),
                                  kCO2_sd = sd(kCO2, na.rm = T),
                                  ECO2 = mean(ECO2_toc * 365, na.rm = T), # in gC/m2/year
                                  ECO2_sd = sd(ECO2_toc * 365, na.rm = T),
                                  kCO2_low_mean = mean(kCO2_low, na.rm = T), # in cm/h
                                  kCO2_low_sd = sd(kCO2_low, na.rm = T),
                                  ECO2_low = mean(ECO2_toc_low * 365, na.rm = T),
                                  ECO2_low_sd = sd(ECO2_toc_low * 365, na.rm = T)) %>%
                          mutate(FCO2 = ifelse(lake.category != "(100,Inf]",
                                               ECO2*(cat.lake.area/lake.area.under100*(inland.water-lake.area.over100))*1e6/12.011 * 43.99 * 1e-12, #MtCO2/y. ECO2 multiplied by the proportion of lakes belonging to each category in Norway, lake area *1e6 to convert in m2,
                                               ECO2*lake.area.over100*1e6/12.011 * 43.99 * 1e-12),
                                 FCO2_low = ifelse(lake.category != "(100,Inf]", 
                                                   ECO2_low*(cat.lake.area/lake.area.under100*(inland.water-lake.area.over100))*1e6/12.011 * 43.99 * 1e-12,
                                                   ECO2_low*lake.area.over100*1e6/12.011 * 43.99 * 1e-12)) %>%  #MtCO2/y
  unique()

knitr::kable(binned.nlss, digits = 2, col.names = c("Nation", 
                                                    "Inland water (area in km2)",
                                                    "Area of lakes with A < 100 km2 in the NLS",
                                                    "Area of lakes with A > 100 km2 in the NLS",
                                                    "Lake category (area in km2)", 
                                                    "Number of NLS lakes in the category",
                                                    "NLS lake area in the category",
                                                    "Proportion of the category compared to NLS",
                                                    "mean pCO2 in uatm", 
                                                    "standard deviation for pCO2", 
                                                    "mean kCO2 (Vachon and Prairie, high estimate) in cm/h",
                                                    "standard deviation for kCO2, Vachon and Prairie",
                                                    "mean ECO2 in gC/m/day (Vachon and Prairie)",
                                                    "standard deviation ECO2 (Vachon and Prairie)",
                                                    "mean kCO2 (Cole and Caraco, low estimate) in cm/h",
                                                    "standard deviation kCO2, Cole and Caraco",
                                                    "mean ECO2 in gC/m2/day (Cole and Caraco)",
                                                    "standard deviation ECO2 (Cole and Caraco)",
                                                    "Estimated total FCO2 (Vachon and Prairie)",
                                                    "Estimated total FCO2 (Cole and Caraco)")) %>%
  kable_styling(bootstrap_options = "bordered")

Nation	Inland water (area in km2)	Area of lakes with A < 100 km2 in the NLS	Area of lakes with A > 100 km2 in the NLS	Lake category (area in km2)	Number of NLS lakes in the category	NLS lake area in the category	Proportion of the category compared to NLS	mean pCO2 in uatm	standard deviation for pCO2	mean kCO2 (Vachon and Prairie, high estimate) in cm/h	standard deviation for kCO2, Vachon and Prairie	mean ECO2 in gC/m/day (Vachon and Prairie)	standard deviation ECO2 (Vachon and Prairie)	mean kCO2 (Cole and Caraco, low estimate) in cm/h	standard deviation kCO2, Cole and Caraco	mean ECO2 in gC/m2/day (Cole and Caraco)	standard deviation ECO2 (Cole and Caraco)	Estimated total FCO2 (Vachon and Prairie)	Estimated total FCO2 (Cole and Caraco)
Finland	34515.0	2119.09	14753.82	(0,0.1]	254	15.18	0.72	1266.42	522.93	0.95	0.34	239.76	162.15	0.72	0.34	184.36	138.91	0.12	0.10
Finland	34515.0	2119.09	14753.82	(0.1,1]	254	76.47	3.61	1160.03	447.97	1.10	0.40	239.27	147.16	0.73	0.33	157.06	103.22	0.62	0.41
Finland	34515.0	2119.09	14753.82	(1,10]	191	498.38	23.52	1072.12	311.17	1.41	0.52	262.71	135.15	0.78	0.36	145.35	82.60	4.47	2.47
Finland	34515.0	2119.09	14753.82	(10,100]	51	1529.06	72.16	1077.45	334.01	1.66	0.59	298.41	125.86	0.78	0.33	138.04	61.61	15.58	7.21
Finland	34515.0	2119.09	14753.82	(100,Inf]	35	14753.82		963.51	163.34	2.03	0.74	304.46	122.18	0.81	0.31	121.63	50.39	16.45	6.57
Norway	20221.0	1095.84	1058.40	(0,0.1]	317	19.48	1.78	696.27	287.76	0.61	0.14	64.37	66.46	0.41	0.11	43.15	46.39	0.08	0.05
Norway	20221.0	1095.84	1058.40	(0.1,1]	281	80.26	7.32	659.69	247.35	0.70	0.19	63.63	61.93	0.42	0.12	38.41	38.69	0.33	0.20
Norway	20221.0	1095.84	1058.40	(1,10]	156	356.56	32.54	592.30	182.15	0.70	0.20	57.11	60.33	0.36	0.10	29.86	31.82	1.30	0.68
Norway	20221.0	1095.84	1058.40	(10,100]	25	639.54	58.36	551.21	141.15	0.74	0.26	56.17	71.04	0.34	0.11	25.84	32.90	2.30	1.06
Norway	20221.0	1095.84	1058.40	(100,Inf]	5	1058.40		562.28	109.07	0.71	0.21	47.56	30.91	0.31	0.03	20.75	11.81	0.18	0.08
Sweden	40141.7	4610.49	11680.91	(0,0.1]	1076	54.57	1.18	1080.00	522.47	0.90	0.30	205.49	192.41	0.68	0.28	161.40	163.17	0.25	0.20
Sweden	40141.7	4610.49	11680.91	(0.1,1]	791	292.45	6.34	1102.33	416.90	1.24	0.33	269.52	182.32	0.81	0.26	181.23	134.64	1.78	1.20
Sweden	40141.7	4610.49	11680.91	(1,10]	540	1531.56	33.22	992.61	318.65	1.52	0.41	276.16	178.27	0.84	0.26	154.71	108.17	9.56	5.36
Sweden	40141.7	4610.49	11680.91	(10,100]	113	2731.91	59.25	832.69	262.21	1.69	0.58	236.89	174.08	0.80	0.30	113.22	87.07	14.63	6.99
Sweden	40141.7	4610.49	11680.91	(100,Inf]	17	11680.91		721.26	180.75	1.85	0.70	206.87	162.17	0.73	0.28	81.91	65.15	8.85	3.50

ggplot(nlss)+geom_boxplot(aes(x=lake.category, y = ECO2_toc))+facet_grid(cols = vars(nation))

ggplot(nlss)+geom_boxplot(aes(x=lake.category, y = ECO2_toc_low))+facet_grid(cols = vars(nation))

5.7 Compare with Raymond et al. (2013)

Raymond et al. (2013) estimate the CO2 emissions as gC/m2 land/year. We convert our estimated median CO2 evasion rate from gC/m2/year to gC/m2 land/year by multiplying it by the water area in a given region, and then dividing it by the land area.

Table 9: Evasion rate of CO2 per unit of area (gC/m2/year) and per unit of land area (gC/m2 land/year), low and high estimates

inland.waters.nor <- 20221 * 1e6 # km2 to m2, @SSB
land.nor <- land <- 323806 * 1e6 # km2 to m2, @SSB
inland.waters.swe <- 4014169.92 * 1e4 # ha to m2, @SCB
land.swe <- 444435 * 1e6 # km2 to m2
inland.waters.fin <- 34515 * 1e6 # km2 to m2, @Statfi
land.fin <- 338478 * 1e6 # km2 to m2

tot.water <- inland.waters.nor + inland.waters.swe + inland.waters.fin
tot.land <- land.nor + land.swe + land.fin

mean.eco2.high <- c(median(nlss$ECO2_toc, na.rm = T)*365, #NLSS # in gC/m2/year
                    with(subset(nlss, nation == "Norway"), median(ECO2_toc, na.rm = T)*365),
                    with(subset(nlss, nation == "Sweden"), median(ECO2_toc, na.rm = T)*365),
                    with(subset(nlss, nation == "Finland"), median(ECO2_toc, na.rm = T)*365))

mean.eco2.low <- c(median(nlss$ECO2_toc_low, na.rm = T)*365, #NLSS # in gC/m2/year
                    with(subset(nlss, nation == "Norway"), median(ECO2_toc_low, na.rm = T)*365),
                    with(subset(nlss, nation == "Sweden"), median(ECO2_toc_low, na.rm = T)*365),
                    with(subset(nlss, nation == "Finland"), median(ECO2_toc_low, na.rm = T)*365))                    
                    
land.eco2.high <- c(mean.eco2.high[1]*tot.water/tot.land,
                    mean.eco2.high[2]*inland.waters.nor/land.nor,
                    mean.eco2.high[3]*inland.waters.swe/land.swe,
                    mean.eco2.high[4]*inland.waters.fin/land.fin)

land.eco2.low <- c(mean.eco2.low[1]*tot.water/tot.land,
                    mean.eco2.low[2]*inland.waters.nor/land.nor,
                    mean.eco2.low[3]*inland.waters.swe/land.swe,
                    mean.eco2.low[4]*inland.waters.fin/land.fin)

kable(tibble("Country" = c("All 3", "Norway", "Sweden", "Finland"),
            "Water"= c(tot.water, inland.waters.nor, inland.waters.swe, inland.waters.fin),
            "Land" = c(tot.land, land.nor, land.swe, land.fin),
            mean.eco2.high,
            land.eco2.high,
            mean.eco2.low,
            land.eco2.low),
      col.names = c("Country","Water area, km2", "Land area, km2", "Median ECO2, gC/m2/year", "Median ECO2, gC/m2 land/year", "Median ECO2, gC/m2/year", "Median ECO2, gC/m2 land/year"),
      digits = 2) %>% kable_styling() %>%
  add_header_above(c(" ","Area" = 2, "High estimate" = 2, "Low estimate" = 2))

	Area		High estimate		Low estimate
Country	Water area, km2	Land area, km2	Median ECO2, gC/m2/year	Median ECO2, gC/m2 land/year	Median ECO2, gC/m2/year	Median ECO2, gC/m2 land/year
All 3	94877699200	1.106719e+12	175.38	15.04	106.94	9.17
Norway	20221000000	3.238060e+11	41.15	2.57	24.08	1.50
Sweden	40141699200	4.444350e+11	209.71	18.94	131.65	11.89
Finland	34515000000	3.384780e+11	235.52	24.02	142.98	14.58

knitr::knit_exit()

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